Question

If you add Natalie’s age and Frankie’s age, the result is 44. If you add Frankie’s age to 3 times Natalie’s age, the result is 70. Write and solve a system of equations using elimination to find their ages

Answer 1

Given:

The sum of Natalie’s age and Frankie’s age is 44.

The sum of Frankie’s age and 3 times Natalie’s age is 70.

To find:

The solutions

Explanation:

Let x be Natalie’s age.

Let y be Frankie’s age.

The equations are.

$\begin{gathered} x+y=44...............(1) \\ y+3x=70.............(2) \end{gathered}$

Subtract (1) from (2), we get

$\begin{gathered} 2x=26 \\ x=13 \end{gathered}$

Substitute the x-value in the equation (1) we get

$\begin{gathered} 13+y=44 \\ y=31 \end{gathered}$

Final answer:

Natalie’s age is 13 years.

Frankie’s age is 31 years.