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. (Remember to clearly show your work on your work page.)

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

Mr. Jacobs wants to save over $3,400 for a car. He has a savings account balance of $800 and will make equal weekly deposits for the next 25 weeks.

How much money should Mr. Jacobs deposit each week?

Answers

Answer:

64$

Step-by-step explanation:

Mr. jacobs should deposit $104 a week

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Answers

Answer:

option c

Step-by-step explanation:

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plug in -⅓ into the trinomial. if it gives an answer of 0 then it's a factor

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Answer:

4

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

[tex] \huge {625}^{ \frac{3}{8} } \times {5}^{ \frac{1}{2} } \div 25 \\ \\ = \huge {( {5}^{4})}^{ \frac{3}{8} } \times {5}^{ \frac{1}{2} } \div {5}^{2} \\ \\ = \huge{5}^{ \cancel4 \times \frac{3}{ \cancel8 \: \: \red{ \bold 2}} } \times {5}^{ \frac{1}{2} } \div {5}^{2} \\ \\ \huge= {5}^{ \frac{3}{2} } \times {5}^{ \frac{1}{2} } \div {5}^{2} \\ \\ \huge= {5}^{ \frac{3}{2} + \frac{1}{2}} \div {5}^{2} \\ \\ \huge= {5}^{ \frac{4}{2} } \div {5}^{2} \\ \\ \huge= {5}^{ 2 } \div {5}^{2} \\ \\ \huge= {5}^{ 2 - 2 } \\ \\ \huge= {5}^{ 0 } \\ \\ \huge= 1[/tex]

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Answer:

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Step-by-step explanation:

Rewrite the equation to describe 4 as a function of 8:
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Answers

Answer:

The steps below show how I transformed the equation in the question into standard form, where the slope and y-intercept is clearest. The slope is -1/2 and the y-intercept is 32.

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Answer:

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Step-by-step explanation:

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Do you have a image ?

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Can Smart people Answer this plz.??????? I WILL GIVE BRAINLEST!!!!!!


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Step-by-step explanation:

Answer:

A square has all its angles equal to 90 degrees a rhombus has no 90 degree angles

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Step-by-step explanation:

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Step-by-step explanation:

Answer:

293.83$

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Answer:

$73.77

I'm not sure if I understood the question correctly

explain it in the comments

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FV=$1000×(1+0.1)5

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Step-by-step explanation:

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Answer:

b:-15

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There are 9 num in the set sowe add all the num and the we divide the answer we got

Answer:

The answer is:

b) - 15

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Answer:

Domain: {2,4,5,9}

Range: {-2,0,2,4}

Function: No

Step-by-step explanation:

Domain = x

Range = y

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Answer: x = 1/2

=========================================================

Explanation:

Recall that quadratic form is ax^2+bx+c.

So we need an x^2 term followed by an x term, then a constant at the end.

It may not look it, but the given equation is nearly in quadratic form.

Rewrite 9^(2x) as (9^x)^2

We get this equivalent equation (9^x)^2 - 2*(9^x) - 3 = 0

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---------------------

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Right answer gets brainlist

Answers

B is the answer I think

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