d)) The ratio of the monthly income and expenditure of Sunayana is 5 : 3. If she
increases her income by Rs 5,000 and decreases the expenditure by Rs 3,000, the
new ratio becomes 5:2. Find her income and expenditure.
Answers
Answer:
Sunayana's income is ₹25000 and expenditures are ₹15000.
Step-by-step explanation:
Let i denote the monthly income and e denote the expenditures.
We know that the ratio of the monthly income to expenditure is 5:3. So, we can write the following proportion:
[tex]\displaystyle \frac{i}{e}=\frac{5}{3}[/tex]
Let's multiply both sides by e. This yields:
[tex]\displaystyle i=\frac{5}{3}e[/tex]
We know that when the income is increased by 5000 and the expenditures are decreased by 3000, the new ratio is 5:2. So, we can write the following proportion:
[tex]\displaystyle \frac{i+5000}{e-3000}=\frac{5}{2}[/tex]
Let's multiply both sides by [tex](e-3000)[/tex]:
[tex]\displaystyle i+5000=\frac{5}{2}(e-3000)[/tex]
Since we know that [tex]i=\frac{5}{3}e[/tex], substitute:
[tex]\displaystyle \frac{5}{3}e+5000=\frac{5}{2}(e-3000)[/tex]
So, let's solve for the expenditures. Distribute the right:
[tex]\displaystyle \frac{5}{3}e+5000=\frac{5}{2}e-7500[/tex]
Subtract [tex]\frac{5}{2}e[/tex] from both sides:
[tex]\displaystyle -\frac{5}{6}e+5000=-7500[/tex]
Subtract 5000 from both sides:
[tex]\displaystyle -\frac{5}{6}e=-12500[/tex]
Multiply both sides by -6/5. So, the expenditures are:
[tex]e=\text{Rs }15000[/tex]
We can use the original ratio to find Sunayana's income:
[tex]\displaystyle i=\frac{5}{3}e[/tex]
Substitute 15000 for e. Evaluate:
[tex]\displaystyle i=\frac{5}{3}(15000)=\text{Rs }25000[/tex]
So, Sunayana's income is ₹25000 and expenditures are ₹15000.
And we're done!
Answer: Income = 25000, Expenditures = 15000
Step-by-step explanation:
A ratio of 5:3 can also be written in fraction form as [tex]\dfrac{5}{3}[/tex] (which is in simplified format from [tex]\dfrac{5x}{3x}[/tex]).
Adding 5000 to 5x results in 5x + 5000
Subtracting 3000 from 3x results in 3x - 3000
--> [tex]\dfrac{5x+5000}{3x-3000}[/tex]
The new ratio of 5:2 can be written in simplified fraction form of [tex]\dfrac{5}{2}[/tex].
Set the fractions equal to each. Then cross multiply and solve for x.
[tex]\dfrac{5x+5000}{3x-3000}=\dfrac{5}{2}[/tex]
5(3x - 3000) = 2(5x + 5000) Cross multiplied
15x - 15000 = 10x + 10000 Distributed
5x - 15000 = 10000 Subtracted 0x from both sides
5x = 25000 Added 15000 to both sides
x = 5000 Divided 5 from both sides
The original ratio of 5 : 3 --> 5x:3x
where 5x is the income and 3x is the expenditures results in:
income = 5x expenditures = 3x
= 5(5000) = 3(5000)
= 25000 = 15000
Related Questions
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please this is urgent
Answers
Answer:
the sum of this equation would equal 23875
The perimeter of a rectangle is 600 yards. What are the dimensions of the rectangle if the length is 30 yards more than the width?
Answers
Answer:
L=165 W=135
Step-by-step explanation:
I plugged in numbers till I found the right fit or you could use the equation P=L+W
Answer: Length of one side: 165 Width of one side: 135
Step-by-step explanation: hope this helps
Could anyone prove this question correct... pls... I will mark branliest for step by step solution.
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Answer:
C
Step-by-step explanation:
the answer is 15. hope this helps
What is the slope of the line?
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Answer: I believe it 8/5
Kennedi paid $288 for 4 nights at a hotel.
Answers
Answer:
$72 per night
Step-by-step explanation:
288/4
Kennedi paid 72 dollars a night :)
$2.99 for 20 shells
question:
Answers
Answer:
$0.15 per shell
Step-by-step explanation:
$2.99/20 = 0.1495
Because we are dealing with money we round to the nearest cent whic is in the tens place
3x +y = 9.x, solve for x
Answers
Answer:
3-y=x
Step-by-step explanation:
Angles 3 and 5 are what type of angle pair?
Answers
Answer:
interior opposite angles
Step-by-step explanation:
they are inside of the shape but on opposite sides (and i did this freshman year)
Answer:
alternate interior angles
Step-by-step explanation:
∠ 3 and ∠ 5 are alternate interior angles.
These angles are on the opposite ( alternate ) sides of the transversal and are in between ( in the interior ) of the parallel lines.
Which type of discontinuity exists at x=0?
Answers
Answer:
removable
Step-by-step explanation:
f(x) = cos(1/x^2) at x = 0;
For the function f(x) = cos(1/x^2) let's substitute the value of 0 in for x...
= cos(1/(0)^2)
= cos(1/0)
Now remember that x/0 is undefined. Removable discontinuity is undefined at the point x₀, and hence our solution is "removable."
WILL MARK BRAINLIEST. Find my mistake and explain how you would fix it. I’ve included step numbers so you can describe where the step is in the solution path.
Answers
A student finished a 30 question test in 75 minutes. Which rate best represents the relationship between the number of minutes spent on test questions and the number of questions?
F. 0.4 minutes per question
G. 2.5 questions per minute
H. 30 questions per minute
J. 2.5 minutes per question
Answers
Answer:
2.5 minutes per quesiton
Step-by-step explanation:
75 minutes to take 30 quesitons means you divide the time equally so
75/30
PLEASE HURRY XX
Find a equation that matches the graph.
Answers
Answer:
x ≥ 3
Step-by-step explanation:
The closed dot represents ≥ and ≤
The dot is located on the number "3"
The closed dot essentially shows that the solution is nothing more than 3 and up.
Let "x" be the variable we use.
x ≥ 3
Best of Luck!
The above never line shows the possible values of an variable in any expression.
Through Observation:
The arrow pointing from 3 to infinity.3 is represented by a closed dot.The value is starting from 3 to infinity.Hence, the required value of the variable can be equal to 3 or greater than 3 for that expression. This can be written as:
[tex] \large{ \boxed{ \rm{ x\geqslant 3}}}[/tex]
Carry On learning !
What is 60 tens in standard form answers are 60,000 69 600 6,000
Answers
Answer:
I think it's 696,000
Explanation:
I can't be sure but is this a troll question... if so that great. :D
Please mark brainliest UwU
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Answers
Answer:
x=6?
Step-by-step explanation:
it is 90 degresses
A = πab/4 solve for b
Answers
Answer:
4A/ (πa) = b
Step-by-step explanation:
A = πab/4
Multiply each side by 4
4A = 4πab/4
4A = πab
Divide each side by πa
4A/(πa) = πab/ πa
4A/ (πa) = b
what is the difference between an independent variable and a dependent variable and how does the independent and dependent variables relate to a graph
Answers
Answer:
Remember, the values of both variables may change in an experiment and are recorded. The difference is that the value of the independent variable is controlled by the experimenter, while the value of the dependent variable only changes in response to the independent variable
Step-by-step explanation:
Answer:
The independent variable is the cause. Its value is independent of other variables in your study. The dependent variable is the effect. Its value depends on changes in the independent variable.
Step-by-step explanation:
HELP ME IM LOST :/
In the diagram, QRSTU is a regular pentagon and STVW is
a straight line. PQVW is a part of a regular polygon. Find
the number of sides of the regular polygon.
Answers
Answer:
15 sides
Step-by-step explanation:
Recall the following about interior and exterior angles of polygons.
Interior angles of polygons:
The formula (n - 2)180 gives the sum of the measures of the interior angles of a polygon of n sides.
If we know the number of sides, we can find the sum of the measures of the angles.
Exterior angles of polygons:
The sum of the measures of the exterior angles of a polygon is 360. If the polygon is a regular polygon of n sides, then the measure of each exterior angle is 360/n.
This problem:
QRSTU is a regular pentagon.
The sum of the measures of the sides of a polygon of n sides is
(n - 2)180
For a pentagon, n = 5, so
(n - 2)180 = (5 - 2)180 = (3)180 = 540
The sum of the measures of the angles of pentagon QRSTU is 540.
Since it's a regular polygon, each angle measures 540/5 = 108.
Angles UQR, R, and S are interior angles of the pentagon, so each one measures 108 degrees.
Now look at polygon VQRS. It is a quadrilateral with sides VQ, QR, RS, and SV. The sum of the measures of the angles of a quadrilateral (4 sides; n = 4) is
(n - 2)180 = (4 - 2)180 = 2(180) = 360
m<VQU = 12 (given)
m<UQR = 108
m<VQR = m<VQU + m<UQR = 108 + 12 = 120
The angles of quadrilateral VQRS are <VQR, <R, <S ,and <TVQ. Their sum is 360.
<VQR + m<R + m<S + m<TVQ = 360
We now substitute the angle values we know and solve for m<TVQ.
120 + 108 + 108 + m<TVQ = 360
m<TVQ = 24
<TVQ is an exterior angle of the large polygon of which PQ, QV and VW are sides.
The sum of the measures of the exterior angles of a polygon, one per vertex, is 360. For a regular polygon, all exterior angles are congruent, and the measure of each exterior angle is the sum of the the measures of the exterior angles divided by the number of sides.
[tex] measure~of~an~exterior~angle = \dfrac{sum~of~the~measures~of~the~exterior~angles}{number~of~sides} [/tex]
[tex] a = \dfrac{360}{n} [/tex]
We know that the measure of an exterior angle is 24 deg.
[tex] 24 = \dfrac{360}{n} [/tex]
[tex] n = \dfrac{360}{24} [/tex]
[tex] n = 15 [/tex]
Answer: 15 sides
Answer:
15 sides
This was tough.
PLEASE HELP, DUE SOON!!
Answers
Answer:
If your Simplifying the expression the answer would be 243b2
Answer:
angles 3 and 4 are a linear pair
Step-by-step explanation:
3 and 4 are a linear pair because the both make up 180 degrees together.
Help me pleasee thank you so much in advance
Answers
x= 15
Bisector means it cuts it in half so angleABD and angleDBC are equal hence the equation of 2x-3= x+12
Add 3 both sides
2x=x+15
Subtract x both sides
X=15
okay due at noon today, I need help on 11 questions: were doing variables on both sides and learning on how to solve for x, no solutions and Infinite solutions. Also need to show work please.
problems:
1: -3-3=-4(2x+7)
2: 8x+3=8x+27
3: 2(x-4)=7-3x
4: 6(x-6)+4=-32+6x
5: -2x-40=8(1-x)
6: -9-8x=-2(7+4x)
7: 2x+8=2(x+4)
8: x-20=5(7x-4)
9: -4(8+7x=-10-6x
10: 28=+ 8x = 8(x+3) +2
11: -35-7x=-7(x=5)
Answers
Answer:
1: x = -2.75
2: No Solutions
3: x = 3
4: Infinite Solutions
5: x = 8
6: No Solutions
7: Infinite Solutions
8: No Solutions
9: x = -1
10: No Solutions
11: Infinite Solutions
Step-by-step explanation:
1)
[tex]-3-3= -4(2x+7)\\-6= -8x-28\\22= -8x\\x= -2.75[/tex]
2)
[tex]8x+3=8x+27\\0x+3=27\\0x=24\\x = No Solutions[/tex]
3)
[tex]8x+3=8x+27\\2x-8=7-3x\\5x-8=7\\5x=15\\x=3[/tex]
4)
[tex]6(x-6)+4= -32+6x\\6x-32= -32+6x\\0=0\\x = Infinite Solutions[/tex]
5)
[tex]-2x-40=8(1-x)\\-2x-40=8-8x\\6x-40=8\\6x=48\\x=8[/tex]
6)
[tex]-9-8x=-2(7+4x)\\-9-8x=-14-8x\\-8x=-5-28x\\x= No Solutions[/tex]
7)
[tex]2x+8=2(x+4)\\2x+8=2x+8\\0=0\\x = Infinite Solutions[/tex]
8)
[tex]x-20=5(7x-4)\\x-20=35x-20\\-34x=0\\x = No Solutions[/tex]
9)
[tex]-4(8+7x)=-10-6x\\-32-28x=-10-6x\\-22x=22\\x = -1[/tex]
10)
[tex]28+8x = 8(x+3) +2\\28+8x=8x+26\\0=-2\\x = No Solutions[/tex]
11)
[tex]-35-7x=-7(x+5)\\-35-7x=-7x-35\\0=0\\x = Infinite Solutions[/tex]
The graph of y = 4 – StartRoot 2 x EndRoot is shown.
On a coordinate plane, a curved line approaches the grid line at (3, 1.5) and ends at (0, 4).
Which statement about the graph is accurate?
The x-intercept of the graph is (4, 0).
The graph has no y-intercepts.
The maximum of the graph occurs at the y-intercept.
The minimum of the graph occurs at the x-intercept.
Answers
Answer:
A
Step-by-step explanation:
Answer:
C (third option) The maximum of the graph occurs at the y-intercept.
Step-by-step explanation:
We will use the process of elimination
It’s not option 1 because if you graph it using the graphing calculator you can see that the x intercept is 8,0 not 4,0
It’s not option 2 because you can see the y intercept is at 0,4 which means there is a y intercept
It’s not option 4 because the graph continues down even after the x intercept
Which leaves us with option 3
Hope this helps :)
whats the y intercept of a(n)=6(n-1)-5
Answers
Which of these represents the final step to a no solution problem?
1=1
x=2
x=x
2=3
Answers
Answer:
I'm probably incorrect, but I think it's the 3rd one
Sam is flying from Columbus, Ohio to Kralendijk, Bonaire, a distance of 2,488 miles. First, he flies 995 miles to Miami, Florida. He then flies from Miami to San Juan, Puerto Rico, a distance of 1,033 miles. How many miles will he travel flying from Columbus to San Juan? How many more miles does he have to fly to Kralendijk?
Answers
Answer:
460 miles
Step-by-step explanation:
Given
Total = 2488 miles
Miami = 995 miles
San Juan = 1033 miles
Required
Determine the remaining distance
Assuming the points are on a straight path.
The remaining distance is:
Remainder = Total - Miami - San Juan
Remainder = 2488 - 995 - 1033
Remainder = 460 miles
when a figure translated, reflected, or rotated, what’s the same about the original figure and it’s image? what’s different
Answers
Answer:
The size of the figure is still the same, but the positioning on the coordinate grid is different.
Step-by-step explanation:
The size of a figure remains constant when it is translated, reflected, or rotated, but its location on the coordinate grid changes.
What is reflection?A reflection is a type of transformation that involves flipping a shape, known as the preimage, across a line, known as the line of reflection, to produce a new shape (called the image). You can picture what would happen if you turned the form across the line to graph a reflection. The reflection equation of the new reflected graph will be y=f(x), y = f (x) given an equation, y= -f(x), y = -f (x). In other words, the function is just multiplied by 1, which results in a curve that crosses the x-axis.The size of a figure remains constant when it is translated, reflected, or rotated, but its location on the coordinate grid changes.As, it is stated in the description that the size of a figure remains constant when it is translated, reflected, or rotated, but its location on the coordinate grid changes.
Therefore, the size of a figure remains constant when it is translated, reflected, or rotated, but its location on the coordinate grid changes.
Know more about reflection here:
https://brainly.com/question/27979059
#SPJ2
Pls helpppppppppppppppppp
Answers
Answer: 75
Step-by-step explanation:
Multiple all those numbers together and then divide by 3
Answer:
75
Step-by-step explanation:
V=lwh/3 which =5·7.5·6/3 and that equals 225/3 which results in 75
Solve the equation -5+ (-4- 2c ) = 3.
Answers
Answer:
C = -6
Step-by-step explanation:
-5+-4=-9
-9-2c=3
-9+9=0; 3+9=12
-2c=12
12/-2= -6
c = -6
10
MILEAGE OF PETER'S CAR
160
140
Miles Traveled
8 8 8 8 8 8 8 8
60
1 2 3 4 5 6 7 8 9 10
Gallons of Gas
The graph shows the number of miles Peter's car traveled and the gallons of gas used.
Which equation can be used to find the distance in miles, d, that the car can travel on g
gallons of gas? *
(5 Points)
d = 169
d = 309
d=249
d=129
Answers
Answer:
[tex] d = 24g [/tex]
Step-by-step explanation:
The graph shows a proportional relationship between distance travelled in miles and the gallons of gas used. Thus, a simple equation can be written to represent this relationship by simply applying the the equation that describes a proportional relationship.
Equation representing a typical proportional relationship is y = kx, where k is the constant of proportionality.
In this case,
y = distance in miles travelled represented by d
x = gallons of gas used represented by g
k = constant of proportionality which is distance travelled per gallon = [tex] \frac{d}{g} = \frac{120}{5} = 24 [/tex]. (note: to get k, you can use any coordinate pair of a point in the line graph).
Therefore, an equation that can be used to find the distance travelled is:
[tex] d = 24g [/tex]
What is 3.09+ 4.88=?
Answers
Answer:
7.97
Step-by-step explanation:
hope this helps
Please help!!!!! Look at the attachment
Answers
Answer:
x=-6
Step-by-step explanation:
Answer: x= -6
Step-by-step explanation:
You combine the 2 expressions
8x+8=5x-10
move the smallest variable
3x+8=-10
and do what you would normally do
3x=-18
/3
x=-6