Algebra 1 : How to find the solution for a system of equations

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #181 : Equations / Inequalities

We have three dogs: Joule, Newton, and Toby. Joule is three years older than twice Newton's age. Newton is Toby's age younger than eleven years. Toby is one year younger than Joules age. Find the age of each dog.

Possible Answers:

none of these

Joule: 9 years

Newton: 3 years

Toby: 8 year

Joule: 5 years

Newton: Not born yet

Toby: 1 year

Joule: 8 years

Newton: 4 years

Toby: 8 year

Joule: 12 years

Newton: 1 year

Toby: 5 year

Correct answer:

Joule: 9 years

Newton: 3 years

Toby: 8 year

Explanation:

First, translate the problem into three equations. The statement, "Joule is three years older than twice Newton's age" is mathematically translated as

\displaystyle J=3+2N

where \displaystyle J represents Joule's age and \displaystyle N is Newton's age.

The statement, "Newton is Toby's age younger than eleven years" is translated as

\displaystyle N=11-T

where \displaystyle T is Toby's age.

The third statement, "Toby is one year younger than Joule" is

\displaystyle T=J-1.

So these are our three equations. To figure out the age of these dogs, first I will plug the third equation into the second equation. We get

\displaystyle N=11-J+1

\displaystyle N=12-J

Plug this equation into the first equation to get

\displaystyle J=3+2(12-J)

\displaystyle J=3+24-2J

\displaystyle J=27-2J

Solve for \displaystyle J. Add \displaystyle 2J to both sides

\displaystyle J+2J=27-2J+2J

\displaystyle 3J=27

Divide both sides by 3

\displaystyle \frac{3J}{3}=\frac{27}{3}

\displaystyle J=9

So Joules is 9 years old. Plug this value into the third equation to find Toby's age

\displaystyle T=J-1

\displaystyle T=9-1

\displaystyle T=8

Toby is 8 years old. Use this value to find Newton's age using the second equation

\displaystyle N=11-T

\displaystyle N=11-8

\displaystyle N=3

Now, we have the age of the following dogs:

Joule: 9 years

Newton: 3 years

Toby: 8 years

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