Question

You have $60 and your sister has $120. You are saving $14 per week and your sister is saving $10 per week. How long will it be before you and your sister have the same amount of money? What amount would you have the same?

Answer 1

15 weeks

$270

Explanation:

Let y = total money saved

x = weeks

I am saving $14 every week, so I multiply x by 14

y = 14x

And I already have $60 to begin with

y = 14x + 60

My sister is saving $10 every week, so I multiply x by 10

y = 10x

And she already has $120 to begin with

y = 10x + 120

Now we just need to find a point where they are the same

14x + 60 = 10x + 120

Move like terms to one side, so subtract 10x from both sides

14x + 60 = 10x + 120

-10x -10x

4x + 60 = 120

Subtract 60 from both sides

4x + 60 = 120

- 60 - 60

4x = 60

Divide both sides by 4

4x/4 = 60/4

x = 15

Now plug in the new x into one of the original equations to find the money amount. We'll use sister's.

y = 10(15) + 120

y = 150 + 120

y = 270