The number of self-propelled mowers and riding mowers who paid total fee of $900 with $20 and $40 each are equal to 5 and 20 respectively.
Let 'x' be the number of self-propelled mowers and 'y' be the number of riding mowers.
Total number of self-propelled and riding mowers = 25
⇒ x + y = 25
⇒ x = 25 - y __(1)
Total fees paid = $900
Rental cost for each self-propelled mower = $20
Rental cost for each riding mower = $40
20x + 40y = 900
⇒ x + 2y = 45___(2)
Substitute the value x in from (1) in (2) we get,
⇒ 25 - y + 2y = 45
⇒ y = 20
⇒ x = 5
Therefore, the number of self-propelled mowers and riding mowers as per given total fee are 5 and 20 respectively.
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When does
expanding and simplifying a(b + c) result in
a positive value for ac?
Expanding the expression a(b + c) = ab + ac, the value of ac is positive if both a and c are positive or if both a and c are negative.
Using Basic Distributive PropertiesBy Multiplying the term outside the brackets by each term inside the brackets
Using this method you can distribute the outer terms into the inner terms. You can multiply the term outside the brackets by the first term inside the brackets. Then multiply the outside term by the second term. If there are more than two tribes, then continue to distribute the tribes until the tribe has no remainder. Keep the signs (positive or negative) in parentheses.
For example:
2(x-3) = 10
2(x) – (2)(3) = 10
2x – 6 = 10
We also know that the distribution characteristic state is a(b + c) = ab + ac.
Because plus times plus is plus and minus times minus is plus. When expanding the phrase a(b + c) = ab + ac, the value of ac is positive if both a and c are positive, and the value of ac is negative if both a and c are negative.
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Convert 9.335 • 10^5 to standard form.
The solution of the given problem of expression comes out to be the standard form of 9.335 × 10⁵ is 933,500.
Expression: What is it?Addition, multiplication, and division in mathematics are required. When united, they produce the following: A mathematical function, some data, and an equation A declaration of fact contains values, parameters, and mathematical operations like additions, subtractions, multiplications, and divisions. It is possible to contrast and evaluate various phrases and words.
Here,
9.335 • 10⁵ is already in standard form, also known as scientific notation, which is a way of representing numbers as a coefficient multiplied by a power of 10.
To clarify, 10⁵ means "10 raised to the power of 5", which is equivalent to multiplying 10 by itself 5 times:
10^5 = 10 x 10 x 10 x 10 x 10 = 100,000
So 9.335 • 10⁵ can be written as:
933,500
Therefore, the standard form of 9.335 • 10^5 is 933,500.
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How much of the circle is shaded? Write your answer as a fraction in simplest form.
3
7
1
2
To subtract two fractions, we must find a common denominator and subtract the numerators.
Solving the Question
The entire circle represents one whole.
To find the fraction for the shaded region, we must subtract [tex]\dfrac{1}{2}[/tex] and [tex]\dfrac{3}{7}[/tex] from one whole:
[tex]1-\dfrac{1}{2}-\dfrac{3}{7}[/tex]
One whole minus half the whole would leave us with just half:
[tex]\dfrac{1}{2}-\dfrac{3}{7}[/tex]
Now, to find a common denominator, multiply the numerator and denominator of each fraction by the denominator of the other fraction:
[tex]\dfrac{1*7}{2*7}-\dfrac{3*2}{7*2}\\\\= \dfrac{7}{14}-\dfrac{6}{14}[/tex]
Now, subtract normally:
[tex]\dfrac{7}{14}-\dfrac{6}{14}\\\\= \dfrac{1}{14}[/tex]
Answer[tex]\dfrac{1}{14}[/tex]
given the recursive formula for a geometric sequence find the explicit formula
a_(n)=a_(n-1)*3
The explicit rule for the sequence is f(n) = a(3)^n-1
How to determine the explicit rule for the sequence?From the question, we have the following parameters that can be used in our computation:
a_(n)=a_(n-1)*3
The above definitions imply that we simply multiply the current from by 3 to get the next term
This means that the function is a geometric function with the following parameters
Common ratio, r = 3
So, the function is
f(n) = a(3)^n-1
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how many different subsets of {1,2,3,4,5,6,7,8,9,10,11,12} contain at least one element in common with each of the sets {2,4,6,8,10,12}, {3,6,9,12}, and {2,3,5,7,11}? (source: mathcounts)
There are a total of 816 different subsets of {1,2,3,4,5,6,7,8,9,10,11,12} contain at least one element in common with each of the given sets
There are 12 elements in the original set, and each of the three smaller sets has different elements. To find the number of subsets that contain at least one element in common with each of the three sets, we need to count the number of subsets that contain at least one element from each set. To do this, we can consider each set separately and multiply the number of subsets that contain at least one element from each set.
The first set has 6 elements, the second set has 4 elements, and the third set has 5 elements. The number of subsets of the first set that contain at least one element is [tex]2^6-1[/tex]=63, the number of subsets of the second set that contain at least one element is [tex]2^4-1[/tex] =15, and the number of subsets of the third set that contain at least one element is [tex]2^5-1[/tex]=31. The number of subsets of the original set that contain at least one element from each of the three sets is 63 * 15 * 31 = 816.
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if a bakery produces 1,215 cupcakes during a 9 hour shift, what is the production rate of cupcakes per hour?
can u explain it in ratio
Simplify using properties of exponents and radicals. √16g^10
Answer:
[tex]4g^5[/tex]
Step-by-step explanation:
[tex]\sqrt{16g^{10}}=\sqrt{16}*\sqrt{g^{10}}=4g^5[/tex]
Given sin O = - 3/4 and angle O is in Quadrant III, what is the exact value of
cos O in simplest form? Simplify all radicals if needed.
well, we know angle θ is in the III Quadrant, that means the sine or opposite side and cosine or adjacent side are both negative, whilst of course the hypotenuse is just a radius amount thus is always positive.
[tex]\sin(\theta )=\cfrac{\stackrel{opposite}{-3}}{\underset{hypotenuse}{4}}\hspace{5em}\textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - b^2}=a ~~ \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \pm\sqrt{4^2 - (-3)^2}=a \\\\\\ \pm\sqrt{7}=a\implies \stackrel{III~Quadrant}{-\sqrt{7}=a}\hspace{5em} \boxed{\cos(\theta )=\cfrac{\stackrel{adjacent}{-\sqrt{7}}}{\underset{hypotenuse}{4}}}[/tex]
3,7,2,4,7,5,7,1,8,8
What is the mean
a) The mode of the list is 7
b) The median of the list is 7.
c) The mean is 5.4
d) The range is 7
What is the Mean, Mode and Median?
Mean: The mean is the average of a set of numbers, calculated by adding up all the numbers and dividing by the total number of numbers in the set.
Mode: The mode is the most frequently occurring number in a set of numbers.
Median: The median is the middle value in a set of numbers when the set is sorted in ascending or descending order.
a) Mode: The mode of the list is 7, as it is the number that occurs most frequently (3 times).
b) Median: To find the median, the list must first be sorted in ascending order:
1, 2, 3, 4, 5, 7, 7, 7, 8, 8
The median of the list is 7.
c) Mean: The mean is found by adding up all the numbers in the list and dividing by the total number of items:
(3 + 7 + 2 + 4 + 7 + 5 + 7 + 1 + 8 + 8)/10 = 54/10 = 5.4
d) Range: The range is the difference between the largest and smallest numbers in the list:
8 - 1 = 7
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Anya bought some tomatoes with a mass of 1.2 kilograms.
How much heavier are Anya's tomatoes than Nobu's tomato?
The information provided doesn't mention Nobu's tomato, so it's not possible to determine how much heavier Anya's tomatoes are than Nobu's tomato without more information.
then, he wants to fill the tank with water until it's completely full. if he uses 85 8585 marbles, he will have to add 20.9 20.920, point, 9 liters of water. what is the volume of each marble?
a. Each marble has a volume of 0.013 liters.
b. 23.4 liters of water would be necessary if William uses 200 marbles.
a. To determine the volume of each marble, we can use the information that 85 marbles fill a tank with a volume of 20.9 liters of water:
Volume of each marble = (26 liters - 20.9 liters) / 85 marbles = 0.26 liters - 0.247 liters/marble = 0.013 liters/marble
So, each marble has a volume of 0.013 liters.
b. To determine the amount of water necessary if William uses 200 marbles, we can use the formula:
Volume of water = Total volume of tank - Volume of marbles
Volume of water = 26 liters - (200 marbles * 0.013 liters/marble) = 26 liters - 2.6 liters = 23.4 liters
So, 23.4 liters of water would be necessary if William uses 200 marbles.
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Complete question:
William has a 26-liter glass tank. First, he wants to put some marbles in it, all of the same volume. Then, he wants to fill the tank with water until it is completely full. If he uses 85 marbles, he will have to add 20.9 liters of water.
a. What is the volume of each marble?
b. How much water is necessary if William uses 200 marbles?
Identify the letter that represents the following numbers on the number line.
The letter on the number line that stands in for the numerals after it On the number line, B stands for -38.
The number line that displays negative numbers is presented to us. On the number line, we are aware that the number rises as we travel to the right.
As per the data given in the above question are as bellow,
The details provided are as bellow,
We can observe that the number line has a grading scale of 1, meaning that each subsequent mark is separated by one unit.
B is four points away from a 42.
This suggests that to get B, we just need to add 4 to -42.
So:
B = -42 + 4
B = -38
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Note : The complete question would be as bellow,
What integer does the letter B represent on the number line above?
What integer does the letter B represent on the number - 1
2.
Quadrilateral ABCD is a rhombus. Given that mZEDA=35º, what are the measures of mZAED,
mZDAE, and mZBCE ? Show your work.
B
Answer:
For quadrilateral ABCD,
m∠AED = 145°
m∠DAE = 145°
m∠BCE = 145°
Consider the following diagram.
ABCD is a rhombus.
Here, the measure of angle EDA=35º
From the figure we can observe that,
∠AED + ∠EDA =180° ................(Linear pair of angles)
⇒ ∠AED = 180° - 35°
⇒ ∠AED = 145°
Also,
∠DAE + ∠EDA = 180° (Linear pair)
⇒ ∠DAE = 180° - 35°
⇒ ∠DAE = 145°
Now we find m∠BCE
We can observe that ∠BCE and ∠DAE are opposite angles .
So, ∠BCE = ∠DAE
⇒ m∠BCE = 145°
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The complete question is:
Quadrilateral ABCD is a rhombus. Given that m∠EDA=35º, what are the measures of m∠AED, m∠DAE, and m∠BCE
A random sample of 500 adults living in a large county was selected and 304 adults from the sample indicated that the unemployment rate was of great concern. What is the standard error of the sample proportion pˆ
?
The standard error of the sample proportion p is approximately 0.281
The standard error of the sample proportion p can be calculated by taking the square root of the sample proportion's variance, which is given by-
p(1-p)/n, where p is the sample size,
The random sample(n) is equal to 500
The adults who indicate the unemployment is 304
Now the sample proportion
p=304/n
p=304/500
p= 0.608
Now the standard error is
SE= √p(1-p)/n
Now put the value here
SE=√0.608(1-0.608)/500
SE=0.021833
Therefore, the standard error of the sample proportion is 0.0218
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The Tour de France is not a 3500 km race, it is a 3500 km cycling race. The diameter of the bike wheels used in the race must be between 55 cm and 75 cm. To find the minimum number of rotations
The minimum number of rotations required for a 3500 km race is 52,800 rotations.
This is calculated by dividing the total distance of the race, 3500 km, by the circumference of the wheel, which is 2πr, where r is the radius of the wheel. The radius of the wheel must be between 27.5 cm (half of 55 cm) and 37.5 cm (half of 75 cm). So, the minimum number of rotations is given by 3500/(23.14r), where r is the minimum radius of the wheel. Substituting in r = 27.5 cm, we get the minimum number of rotations required for a 3500 km race as 52,800.
To arrive at this result, we must first calculate the circumference of the wheel, which is given by 2πr, where r is the radius of the wheel. Since the diameter of the wheel must be between 55 cm and 75 cm, the radius of the wheel must be between 27.5 cm (half of 55 cm) and 37.5 cm (half of 75 cm).
We then divide the total distance of the race, 3500 km, by the circumference of the wheel, which is given by 2πr. Substituting in the minimum radius of the wheel, 27.5 cm, we get the minimum number of rotations required for a 3500 km race as 52,800.
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Find the volume of the solid generated by rotating the region bounded by y = x^2, y = 0, and x = 1, about the y-axis.
Step-by-step explanation:
To find the volume of this solid, we will use the method of cylindrical shells. We will integrate the cross-sectional area of a cylinder, given by πr^2, over the height of the solid. The height of the solid is given by the difference between the upper and lower bounds of the region, which are y = x^2 and y = 0, respectively. The radius of each cylindrical shell is given by the distance of the cross-sectional circle from the y-axis, which is x.
So, the volume of the solid is given by the integral:
V = ∫[0, 1] π * x^2 dx
Using the antiderivative of π * x^2, which is π * x^3 / 3, we can find the definite integral:
V = (π * x^3)/3 from 0 to 1
Evaluating the definite integral and simplifying, we get:
V = π/3 units^3
So, the volume of the solid is π/3 units^3.
Answer:
Step-by-step explanation:
Find the volume of the solid generated by rotating the region bounded by y = x^2, y = 0, and x = 1, about the y-axis.
9.5% of Undergraduate students study abroad. 60% of those who study abroad are female. 49 % of those who do not study abroad are female. calculate probability of a female student studying abroad .
The probability that the student is female and studying abroad is equal to 0.057. It means 5.7% of student is female studying abroad.
Given,
Undergraduate students who study abroad = 9.5% = 0.095 undergraduate
female students who travel for study. = 0.60
male undergraduates who travel for study. = 0.40
undergraduate female students who do not study abroad. = 0.49
Those male undergraduates who do not study abroad. = 0.51
Probability refers to potential. It is a field of mathematics that generally examines how the random events happen. The value is expressed as a number between 0 and 1. To determine how likely an event is to occur, probability has been introduced in mathematics.
We know that ,
the probability that the student is female and studying abroad =
0.60 * 0.095 = 0.057
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Find the sum: 7/10 + 11/100
A: 18/10
B: 81/ 100
C: 70/100
D: 18/110
Answer:
81/100
Step-by-step explanation:
First we need to find a common multiple of 10 and 100. It's going to be 100, so we chance 7/10 to 70/100.
Now that the denominator matches for both of them, now we add.
70/100 + 11/100 = 81/100
1. Sandra read 5 books, Deacon read 6 books and Breanna read 7 books. One book was read by all three children, but every other book was different. How many different books did the children read? 2. In Science class, Sara needed 8 test tubes for 3 different experiments. The first experiment required 2 test tubes and the other two experiments required the same number of test tubes. How many test tubes were needed for each of the other two experiments? 3. Multi-Step Word Problems 4. 6. Branson and his sister Beatrice combined their allowance of $7 each, so they could buy a movie for $12. They bought $1 containers of fruit salad with the remaining money and split the containers evenly between them. How many containers of fruit salad did they each get? Before Cam broke his right arm, he was able to type 9 words per minute on his phone. After he broke his arm, he had to use his left hand for a while, and he could only type 6 words per minute. What is the difference between the number of words he could type in 5 minutes before and after he broke his arm. 5. When Gisselle decided to stop eating junk food, she started saving more of her allowance to buy a larger bicycle. She managed to put away $6 every week for 8 weeks and found a nice used bicycle for $50. She thought that she had close to that amount in her savings jar. Did she have exactly enough for the bicycle? If not, how much extra or how much too little did she have? Annie and Dustin took a beginner's programming course over several weekends that showed them how to make simple video games. They spent most of their waking hours engaged in programming tasks and ended up with a game they called "Ro-Bot- Ro-Call." How many hours do you think they spent on their course? Show your work. Math-Drills.com
Answer:
Step-by-step explanation:
Sandra, Deacon, and Breanna read a total of 5 + 6 + 7 = 18 books. Since one book was read by all three children, we need to subtract it once from the total. Therefore, they read 18 - 1 = 17 different books.
Sara needed 8 test tubes for 3 different experiments. The first experiment required 2 test tubes, leaving 8 - 2 = 6 test tubes for the other two experiments. Since the two experiments required the same number of test tubes, each one required 6/2 = 3 test tubes.
It is unclear what the question is asking. Please provide more information or a specific question.
Branson and his sister Beatrice combined their allowance of $7 each to buy a movie for $12. They spent a total of 7 x 2 = $14 on the movie. Therefore, they had 14 - 12 = $2 left to buy fruit salad. They bought 2 containers of fruit salad for $1 each, leaving them with $0. They split the containers evenly between them, so each of them got 2/2 = 1 container of fruit salad.
Before Cam broke his right arm, he could type 9 words per minute on his phone. After he broke his arm, he could only type 6 words per minute. The difference between the number of words he could type in 5 minutes before and after he broke his arm is 5 x (9 - 6) = 5 x 3 = 15 words.
Gisselle saved $6 every week for 8 weeks, so she saved a total of 6 x 8 = $48. She found a used bicycle for $50, so she did not have exactly enough for the bicycle. She was $50 - $48 = $2 short.
What is the slope of the line below?
The slope is -2/5
You have a point at (0,3) and (5,1). If you create a slope triangle, it'll go down 2 and right 5.
need help with this question
Answer:
D
Step-by-step explanation:
A and B would move the functional graph unchanged 6 units up and down.
but that is clearly not what happened.
so, A and B are out.
h(x) is instead f(x) shifted 6 units to the left.
that means the functional value h(x) is the same as f(x') just 6 units "earlier". that means x = x' - 6 or x' = x + 6.
therefore,
h(x) = f(x + 6) = sqrt(x + 6)
**Jordan has an annual salary of $102,000. His monthly expenses include a $2,600 mortgage payment, a $250 lease payment, $500 in minimum credit card payments, and a $400 payment on his speed boat. He also receives $1,200 in interest from his savings and other accounts each month. Calculate Jordan's DTI (debt-to-income) ratio to the nearest tenth. Hint: when calculating Jordan's DTI divide his total monthly expenses by his total monthly income from all sources of income (which also includes the interest he receives). a. 33.4% b. 38.7% c. 40.2% d. 45.7%
The answer is 38.7% which is option b., is Jordan's DTI (debt-to-income) ratio to the nearest tenth.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
To calculate Jim's DTI (debt-to-income) ratio, we need to divide his total monthly debt payments by his gross monthly income.
His total monthly debt payments are:
$2,600 (mortgage payment)
$250 (lease payment)
$500 (credit card payments)
$400 (speed boat payment)
then,
Total Monthly Debt Payments = $3750
now,
His gross monthly income is his annual salary of $102,000 divided by 12 months which is $8,500
we get,
DTI = Total Monthly Debt Payments / Gross Monthly Income
= $3,750 / $8,500 + 1200
=0.387
=38.7%
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if you believe bit plane slicing is lossy, can 1st-order extrapolation or 2d bilinear interpolation recover the original image?
If you believe that bit plane slicing is lossy, then 1st-order extrapolation or 2D bilinear interpolation cannot fully recover the original image.
What is extrapolation and interpolation?
Extrapolation is an estimation based on extending a known sequence of data beyond what is absolutely known.
Interpolation is the estimation of a value in a sequence of values between two known values.
Bit plane slicing is a lossy compression technique, which means that some information from the original image is lost during the compression process. The purpose of bit plane slicing is to reduce the size of an image by removing less significant bits from each pixel. As a result, the quality of the image is reduced.
1st-order extrapolation and 2D bilinear interpolation are techniques used to estimate or predict missing or unknown values from a given set of data. These techniques can be used to enhance the quality of an image, but they cannot recover the original image in cases where information has been lost through compression or degradation. In other words, they can only improve the quality of the image to a certain extent, but they cannot restore it to its original state.
So, if you believe that bit plane slicing is lossy, then 1st-order extrapolation or 2D bilinear interpolation cannot fully recover the original image, although they may help to improve its quality to some extent.
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The width of a rectangle is 6.25x - 3.5 feet and its length is 3.5x + 6 feet. Find the perimeter of the rectangle
Answer:
see below
Step-by-step explanation:
perimeter = 2*(6.25x - 3.5 + 3.5 x +6) =2(9.75x+2.5) = 19.5x+5
What is the most common measuring system in the world?
English
Metric
Apothecary
None of the above
Metric System is a decimal system of measurement that is based on the meter, kilogram, and second and is used in most countries around the world. It is also known as the International System of Units (SI).
The Metric System is the most common measuring system used in the world today. It is a decimal system based on the meter, kilogram, and second and is officially known as the International System of Units (SI). This system was initially developed in France in the late 18th century and is now used in most countries around the world. The Metric System is based on powers of 10 and each unit is related to the next unit by a factor of 10. For example, a kilometer is equal to 1000 meters, a milliliter is equal to 0.001 liters, and a centimeter is equal to 0.01 meters. The Metric System is used to measure length, area, mass, weight, temperature, and volume. It is used in many different industries and applications including science, engineering, medicine, and agriculture. The Metric System has become the international standard for scientific measurements and is accepted by most countries as the preferred system of measurement. The Metric System is also easier for students to learn and use than other systems of measurement.
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Lexi and Ann go shopping. Ann wonders how much tax she will have to pay on her purchase of $76. Lexi says, "They just charged me $14.50 in taxes when I bought these outfits for $200." How much will Ann pay in taxes?
well, first off, let's see how much was it in tax for the $200 purchase, since we know it was a whooping $14.50.
now, if 200(origin amount) is the 100%, what's 14.50 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 200 & 100\\ 14.50& x \end{array} \implies \cfrac{200}{14.50}~~=~~\cfrac{100}{x}\implies 200x=1450 \\\\\\ x=\cfrac{1450}{200}\implies x=\stackrel{\%}{7.25}[/tex]
now, let's check how much will that be for $76
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{7.50\% of 76}}{\left( \cfrac{7.50}{100} \right)76}\implies 5.7[/tex]
A long distance space probe takes off from earth heading towards Proxima centauri and travels 1.7 light years what are the additional distances the pro can travel for getting to the star
The distance of the probe is given by the equation A = 2.546 light years
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
The distance traveled by the space probe = 1.7 light years
Now , the value of 1 light year = 9.461 x 10¹³
So , the distance traveled by the space probe = 1.7 x value of 1 light year
On simplifying the equation , we get
The distance traveled by the space probe D = 1.7 x 9.461 x 10¹³
The distance traveled by the space probe D = 16.0837 x 10¹³ km
The distance traveled by the space probe D = 1.60837 x 10¹⁴ km
The distance to Proxima Centauri = 4.246 light years
So , the remaining distance is A = distance to Proxima Centauri - distance traveled by the space probe
On simplifying the equation , we get
The remaining distance is A = 2.546 light years
Hence , the equation is A = 2.546 light years
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WILL GIVE BRAINIEST HELP ASAP DUE IN 20 MIN
in isosceles triangle ABC AC is equal to BC is equal to 8 centimetres the vertical height CD of the triangle is 5 cm calculate the length of the base ab
The length of the base, AB, can be found to be 12. 49 cm
How to find the base length ?The base length can be found using the Pythagoras Rule which is:
c ² = a ² + b ²
a = CD which is the height
c = AC
So we can find half od base length when we divide the shape into a right angled triangle :
8 ² = 5 ² + b²
b ² = 64 - 25
b = √ 39
b = 6. 24 cm
Double of this would be:
= 12. 49 cm
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3. Mr. Sanchez’s class sold fruit pies for $1.45 each and Mr. Kelly’s class sold bottles of fruit juice for $1.25 each. Together, the classes sold 53 items and earned $70.85 for their school.
(a) Write and solve a system of equations that model the problem. Show all your work.
(b) Which class earned more money?
(c) How much more money did that class earn?
Let x be the number of fruit pies sold by Mr. Sanchez's class, and y be the number of bottles of fruit juice sold by Mr. Kelly's class.
(a) We can set up a system of equations to model the problem:
x + y = 53 (total number of items sold)
1.45x + 1.25y = 70.85 (total amount earned)
To solve this system using substitution, we can rearrange the first equation to solve for one variable in terms of the other:
x + y = 53
x = 53 - y
Then substitute x = 53 - y into the second equation:
1.45x + 1.25y = 70.85
1.45(53 - y) + 1.25y = 70.85
76.85 - 1.45y + 1.25y = 70.85
0.2y = 6
y = 30
Substituting y = 30 into the equation x + y = 53 gives:
x + y = 53
x + 30 = 53
x = 23
So Mr. Sanchez's class sold 23 fruit pies and Mr. Kelly's class sold 30 bottles of fruit juice.
(b) To find out which class earned more money, we can calculate the total amount earned by each class:
Mr. Sanchez's class: 1.45 x 23 = $33.35
Mr. Kelly's class: 1.25 x 30 = $37.50
Mr. Kelly's class earned more money.
(c) The amount by which Mr. Kelly's class earned more than Mr. Sanchez's class is:
$37.50 - $33.35 = $4.15