Question

John started working part time at a local pet store and earned $24 a day. Two days later

Jack started working part time at a local music store and earned $30 a day. After how

many days do they earn the same amount?

Answer 1

They earn the same amount after 8 days.

Explanation:

When both started working(the day Jack started, John had been working for 2 days earning $24 a day, so he already had 2*24 = $48). We started modeling from this day.

John:

He already had $48.

He would earn $24 per day.

So after n days, his amount would be:

`A_(Jo)(n) = 48 + 24n`

Jack:

He has nothing.

He would earn $30.

So after n days, his amount would be:

`A_(Ja)(n) = 30n`

After how many days do they earn the same amount?

After n days.

n is found when:

`A_(Jo)(n) = A_(Ja)(n)`

`48 + 24n = 30n`

`6n = 48`

`n = (48)/(6)`

`n = 8`

They earn the same amount after 8 days.