Question

Janelle has $20 and is saving $6 per week. April has $150 and is spending $4 per week. When will they both have the same amount of money?

Answer 1

After `13` weeks

Explanation:

Janelle starts with `20`, and gains `6` per week. So, after `w` weeks, she will have gained `6w`, for a total amount of

`J = 20+6w`

Similarly, April starts with `150`, and loses `4` per week. So, after `w` weeks, she will have lost `4w`, for a total amount of

`A = 150 - 4w`

We wonder when they will have the same amount of money, so:

`J = A \iff 20+6w=150 - 4w`

Add `4w` to both sides:

`20+10w = 150`

Subtract `20` from both sides:

`10w = 130`

Divide both sides by `10`:

`w = 13`