Juan is three times as old as Gabe and Gabe is six years older than Catherine. If the sum of their ages is 149, how old is each person? Define a variable, write an equation, solve the equation, and answer in a complete sentence.

Answers

Answer 1

Answer:

Juan = 93 years.

Gabe = 31 years.

Catherine = 25 years.

Step-by-step explanation:

Let the age of Juan = J

Let the age of Gabe = G

Let the age of Catherine = C

Translating the word problem into an algebraic equation, we have;

[tex] J = 3G[/tex] ..........equation 1

[tex] G = C + 6 [/tex] ........equation 2

[tex] J + G + C = 149 [/tex] ........equation 3

We would solve the linear equations by using the substitution method;

Substituting equation 2 into equation 1;

[tex] J = 3(C + 6)[/tex]

[tex] J = 3C + 18[/tex] ........equation 4

Substituting equation 2 and equation 4 into equation 3;

[tex] (3C + 18) + (C + 6) + C = 149 [/tex]

Simplifying the equation, we have;

[tex] 5C + 24 = 149[/tex]

[tex] 5C = 149 - 24[/tex]

[tex] 5C = 125[/tex]

[tex] C = \frac {125}{5}[/tex]

C = 25 years.

To find G; from equation 2

[tex] G = C + 6[/tex]

Substituting the value of "C" into equation 2, we have;

[tex] G = 25 + 6[/tex]

G = 31 years.

To find J; from equation 1

[tex] J = 3G [/tex]

Substituting the value of "G" into equation 1, we have;

[tex] J = 3 * 31[/tex]

J = 93 years.

Therefore, Juan is 93 years old, Gabe is 31 years old and Catherine is 25 years old.


Related Questions

)
11
12
Which is a reasonable first step that can be used to solve the equation 4x+3(x+2) = 5(2x-3)
O Distribute the 3 to x + 2, and distribute the 5 to (2x - 3).
O Combine 4x and x on the left side of the equation.
© Apply the subtraction property of equality to move the 2 from the left to the right side of the equa
O Apply the addition property of equality to move the 3 from the right to the left side of the equation

Answers

A should be the answer

Answer:

D

Step-by-step explanation:

At a farm, four employees harvest 48 pounds of food over a certain number of hours. Each employee works the number of hours shown. Employee A6 Employee B :4 employee C:8 employee D:8 The number of pounds of food harvested by each employee is potential to the number of hours worked.

Answers

Answer:

A harvest = 11 pound (Approx)

B harvest = 7 pound (Approx)

C harvest = 15 pound (Approx)

D harvest = 15 pound (Approx)

Step-by-step explanation:

Given:

A - 6

B - 4

C - 8

D - 8

Total harvest = 48 pound

Computation:

Total hour = 6+4+8+8

Total hour = 26 hour

A harvest = 48(6/26)

A harvest = 11 pound (Approx)

B harvest = 48(4/26)

B harvest = 7 pound (Approx)

C harvest = 48(6/26)

C harvest = 15 pound (Approx)

D harvest = 48(6/26)

D harvest = 15 pound (Approx)

Multiply out 3(2x-7)

Answers

Answer:

6x-21

Step-by-step explanation:

3*2x = 6x

3*-7 = -21

6x-21

The answer is 6x-21, multiply the equation with distributive property


Find the exact value of sec 3pi/2
If not defined, write undefined.

Answers

Answer: Undefined

Step-by-step explanation:

Sec 3[tex]\pi[/tex]/2 = 1/Cos(3[tex]\pi[/tex]/2) = 1/0 = Undefined

Multiply ()
Part A: What is/are the restricted value(s)?
Part B: What factor(s) can be eliminated before multiplying?
Part C: What is the simplified product?
Select all answers that apply for Part A and Part B, and select one answer for Part C.

C: 3x-12
———-
x^2+2^x

B: x+2

C:(x-4)(15x)
————-
(5x^2)(x+2)

A: -2

C: 3x-12
-———
x+2

A: 0

A: 5

C: 3x-6
———
x

A: -4

A: 2

B: x

A: 4

B: 5

B: x^2

Answers

Answer:

Step-by-step explanation:

b, i'm not sure but thats what i think.

A'B'C' is the image of ABC after a translation. Write the rule for the translation. (x,y) → ______

Answers

Answer:

A hint because i am still finding the answer, ● TRANSLATION is a transformation that SLIDES a figure horizontally (left or right), vertically (up or

down), or both on a coordinate plane.

OVER 2 1/2 UP 1/2. THIS SHOULD BE RIGHT BUT A SECOND OPINION IS GOOD TOO.

In my town, gas prices are always listed to the thousandths place. Since the smallest coin we have is the penny, we have to round them to the hundredths place. If the price of gas is $8.162, what will the price be when we round it to the hundredths place?

Answers

I believe the answer is $1.16 but sorry if this is wrong!

The math club is having a car wash to raise funds to attend a state competition they need to raise a minimum of $325 the cost of supplies for the car wash is $25 if they except 40 cars on the wall on the day of the car wash what is the amount they have to charge each car to meet the minimum goal what is the answer

Answers

Answer:

£8.75

Step-by-step explanation:

325+25=350

350/40=8.75

Which of the following values are solutions to the inequality −4≥5x−3?

Answers

Answer:

X[tex]\leq[/tex] -1/5

Step-by-step explanation:

I hope it helps

Find the sum of the finite geometric series

6 - 4 + 8/3 - 16/9 + 32/17

Answers

Answer:

The sum of geometric series 6 - 4 + 8/3 - 16/9 + 32/17 is 4.0416

Step-by-step explanation:

We need to find the sum of geometric series 6 - 4 + 8/3 - 16/9 + 32/17

The formula used to find sum of geometric series is [tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]

where a is 1st term, n is number of terms and r is common ratio

so, in the given geometric series 6 - 4 + 8/3 - 16/9 + 32/17 we have

First Term a=6

Common ratio r= -0.6

Number of terms n= 5

Putting values in formula to find sum of given geometric series

[tex]S_n=\frac{a(1-r^n)}{1-r}\\S_n=\frac{6(1-(-0.6)^5 )}{1-(-0.6)}\\S_n=\frac{6(1-(-0.07776))}{1+0.6}\\S_n=\frac{6(1+0.07776)}{1.6}\\S_n=\frac{6.46656}{1.6}\\S_n=4.0416[/tex]

So, the sum of geometric series 6 - 4 + 8/3 - 16/9 + 32/17 is 4.0416

What is the slope of the line

Answers

Answer:

2 over 2. which would simplify to 1. rise over run.

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

slope = change in y over change in x

the line goes down 1 and over 1 so slope is -1/1 or -1

please help me, solve for n

Answers

Answer:

The value of n will be:

[tex]n=\frac{89}{4}[/tex]

Step-by-step explanation:

Given the expression

[tex]\frac{n}{2}-8^{-1}=11[/tex]

Apply the exponent rule:

[tex]a^{-1}=\frac{1}{n}[/tex]

so the expression  becomes

[tex]\frac{n}{2}-\frac{1}{8}=11[/tex]

Add 1/8 to both the sides

[tex]\frac{n}{2}-\frac{1}{8}+\frac{1}{8}=11+\frac{1}{8}[/tex]

[tex]\frac{n}{2}=\frac{89}{8}[/tex]

[tex]n=\frac{89}{4}[/tex]

Therefore, the value of n will be:

[tex]n=\frac{89}{4}[/tex]

Find the slope of the line that passes through
(10, 1) and (5,2)

Answers

Answer:

the slope of the line is -1/5

remember, rise over run.

Step-by-step explanation:

May I have brainliest please? :)

Answer:

[tex]m=-\frac{1}{5}[/tex]

Step-by-step explanation:

Which of the following is NOT a true bi-conditional statement?
A It is noon if and only if it is 12:00 PM.
B Two segments are congruent if and only if they have the same length.
C An angle is right if and only if its measure is 90°.
D I am a violinist if and only if I am a musician.

Answers

d

because your a musician you cant be a true statement I am wrong

Does anyone know how to like graph it for me like just tell me where they go please and thank you!

Answers

Answer:(0,4), (-1,0), (-4,-2)

Step-by-step explanation:

gallons of gas (x) miles (y)
1 30
2 60
3 90

Is there any value of x that would lead to multiple values of y? If so, write down that particular value of x.

Answers

Answer:

There is no x-value that would lead to multiple y-values.

Step-by-step explanation:

PLATO answer

Bob bought 5 books for x dollars each and a DVD for $12. Write an expression for how much money Bob spent.

Answers

Answer:

5x+12

Step-by-step explanation:

X symbolizes how many he is buying plus the extra 12 dollars

Answer:

5x+12=y

Step-by-step explanation:

Y represents the amount of money spent.

if x represents the amount of one book and Bob bought 5 books than you have to multiply the amount of one book by five to get the amount spent on all the books. Thus getting 5x

You need an equation to find how much money spent total. Thus adding $12 because Bob also bought a DVD for $12.

Therefore, the only logical equation is 5x+12=y

The graph below shows a quadratic function f(x) and an absolute value function g(x) Which of the following x-values are approximate solutions to the equations f(x) = g(x)? select all that apply

Answers

Answer:

a, b ,e

Step-by-step explanation:

The solutions to the equation f(x) = g(x) are x = -3.3 and x = 5.2

The correct answers are option (A) and option (E)

What is equation?

"It is a mathematical statement which consists of equal symbol between two algebraic expressions."

What is solution to equations?

"It is a value or a set of values, when substituted for the unknowns, the equation becomes true."

For given question,

We have been given the graph of a quadratic function f(x) and an absolute value function g(x).

We need to find the x-values that are approximate solutions to the equation f(x) = g(x).

To solve the equation f(x) = g(x), we look for the points where the graphs of f(x) and g(x) intersect.

The intersection point of f(x) = g(x) appears to be at point which lie in the second quadrant and the x-value lie between -2 and -4.

Also,  the second intersection point lie in the fourth quadrant where x value is in between 4 and 6.

So, the solutions to the equation f(x) = g(x) are x = -3.3 and x = 5.2

The correct answers are option (A) and option (E)

Learn more about the solution to the equation here:

https://brainly.com/question/14603452

#SPJ2


Is the line through points P(2. - 7) and Q(5, 5) parallel to the line through points R(5, 5) and S(4.1)? Explain.

Answers

Answer:

Yes they are parellel

Step-by-step explanation:

Find the slope of both

5- -7 / 5 - 2 = slope of 4

1 - 5 / 4 - 5  = slope of 4

what is a slope-intercept form of a equation of a line that passes through (-1,6) and (2,-3)

Answers

Answer:

go to m a t h w a y trust me that app is a game changer

What is the Rise Run and Slope

Answers

Answer:

Rise = 2

Run = 1

Slope = 2

Step-by-step explanation:

To find the rise you look at how much the line rises, so you can see it rises 2 after going over 1. So now we know the rise is 2 and the run is 1, because we used 1 as the run to find the rise.

The slope is found by dividing the run from the rise

[tex] \frac{rise}{run} [/tex]

So the slope is 2.

Please what is this I need help

Answers

Answer:

It is B

Step-by-step explanation:

A flea is jumping around on the number line. He starts at 3 and jumps 5 units to the left. Write the integer of where the flea is now on the number line. number line

Answers

Answer:

This is How to solve a integer: Write your number on a piece of paper. You can write your integer in a variety of ways. For instance, write your integer in standard form (such as 63), expanded form (such as 100+50+2, which in standard form would be 152) or in written form (such as one thousand two hundred thirteen).

Step-by-step explanation:

How many repeating digits are in 0 536?

Answers

Are there any repeating digits? There isn’t. Remember, on a device make sure you put 3 dots next to a decimal to show it’s repeating.

Answer:

the answer is 3

Step-by-step explanation:

edge 2020

1. The Willis Tower (formerly known as the Sears Tower) in Chicago is about 1454 feet tall. A model of it has a scale of 2 in = 45 feet. How tall is the model?

Answers

Answer:

[tex]x\approx64.622\text{ inches}[/tex]

Step-by-step explanation:

We can write a proportion that relate the model lengths to the actual length. The traditional format is:

[tex]\frac{\text{Model Length}}{\text{Scale Factor}}=\frac{\text{Original Length}}{\text{Scale Factor}}[/tex]

Hence, we will substitute 1454 for the “Original Length.”

2in for the “Scale Factor” below the model.

And 45ft for the “Scale Factor” below the original.

Let the model length be x.

This yields:

[tex]\frac{x}{2}=\frac{1454}{45}[/tex]

Solve for x. Cross-multiply:

[tex]2908=45x[/tex]

Divide both sides by 45:

[tex]x\approx64.622\text{ inches}[/tex]

Therefore, the height of the model is about 64.6 inches.

Step-by-step explanation:

solution

we know that,

tower hight = 1454 feet

here

2inch=45 feet

now,

1454 feet=(1454/45)inch

1454 feet =32.31 inch

so,tower is 32.31 inch tall according to model length

this may help you (:

5 pounds of apples cost $12. How many pounds of apples can you buy for $1.

Answers

Answer:

5/12 or 0.41666667 pound

Step-by-step explanation:

Set up the equation as 5/12=x/1 and cross multiply. Then you will get 12x=5. Divide both sides by 12 and then you will get 5/12.

Answer:

5/12 of a pound or 0.42 pounds

Step-by-step explanation:

$1 is 12 times less than $12. So, if the amount of money is divided by 12, than the amount of apples you can buy is also divided by 12:

5/12 = 0.42

You can buy 5/12 of a pound or approximately 0.42 pounds of apples for $1.

GIVING BRAINLEST PLSS HELP MEEEEEEEEEEEE

Answers

Answer:

b is correct

hope that helped if yes give me brainliest and if no draw my attention by hitting the comment section

Answer:

b

Step-by-step explanation:

Rob is buying some green apples to make some fresh apple juice. The price of the green apples is G and Rob has a coupon for 10% off. Consider the expressions given in the answers. Which expression is the price of the green apple after using the coupon?
A) 1.1g
B) 0.1g
C) g – 0.1g
D) g
E) g – 0.1

Answers

C) g-0.1g
You multiply gx0.1 then subtract that from the price of apple (g).

Answer:

c

Step-by-step explanation:

Sarah and 2 friends go out to eat to a restaurant. Their bill is $89.50. In addition to the bill, they are going to leave a 20% tip and pay 5% in
taxes. If they decide to split the bill, how much will each person pay?
Blank 1:

Answers

Answer:

$111.87

Step-by-step explanation:

so you are going to divide this bill between two people. first you are going to divide 89.50 and divide it by 100. the answer you get you will multiply that by 20. that will be the tip they give so add that to 89.50. for the taxes you do the same but instead of multiplying by 20 you will multiply by 5. you are going to have to add that all up and then divide by 3.

Answer:

$111.87

Step-by-step explanation:

can someone help me with this :( , it’s similar triangles btw

Answers

HOPE THIS HELPS YOU

I KNOW THAT THESE TRIANGLES ARE SIMILAR BY THE WAY...

Answer:

The triangles are propotional

Step-by-step explanation:

FH = 45 = 5

BC 27 3

GH = 22.5 = 5

BD 13.5 3

GF = 30 = 10 = 5

CD 18 6 3

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