Question

Asia and Addison are saving for a new cell phone. Ava is starting with a $100 adding $5 each week. Addison is starting with $200 adding $4 each week. Write and solve a system that can be used to find out after how many weeks Ava and Addison will have the same amount of money saved.

Answer 1

Equations

Ava and Addison are saving for a new cell phone.

Ava starts with $100 and adds $5 each week.

Let's call x to the number of weeks, thus the equation to model the amount of money of Ava's is:

A = 100 + 5x

Addison starts with 200 and adds $4 each week, thus the equation of the money he/she has is:

B = 200 + 4x

We are required to find the number of weeks needed for them to have the same amount of money saved, that is:

100 + 5x = 200 + 4x

Subtracting 4x:

100 + 5x - 4x = 200

Subtracting 100:

5x - 4x = 200 - 100

Operating:

x = 100

Ava and Addison will have the same amount of money saved in 100 weeks

Ava will have: 100 + 5(100) = $600

Addison will have: 200 + 4(100) = $600