Question

Richard has $20 and is saving $2 a month. Scarlett has $50 but is spending $3 a month.

Write and solve a system of equations to show when they will have the same amount of money.

Answer 1

Let's use R to represent Richard's savings and S to represent Scarlett's savings after t months.

For Richard:

R = 20 + 2t

For Scarlett:

S = 50 - 3t

We want to find when R is equal to S. So we can set up the following equation:

20 + 2t = 50 - 3t

Adding 3t to both sides:

20 + 5t = 50

Subtracting 20 from both sides:

5t = 30

Dividing both sides by 5:

t = 6

Therefore, it will take 6 months for Richard and Scarlett to have the same amount of money. At that time, Richard will have saved:

R = 20 + 2t = 20 + 2(6) = 32

And Scarlett will have saved:

S = 50 - 3t = 50 - 3(6) = 32

So they will both have $32.