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?

Respuesta :

Answer:

They earn the same amount after 8 days.

Step-by-step 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:

[tex]A_{Jo}(n) = 48 + 24n[/tex]

Jack:

He has nothing.

He would earn $30.

So after n days, his amount would be:

[tex]A_{Ja}(n) = 30n[/tex]

After how many days do they earn the same amount?

After n days.

n is found when:

[tex]A_{Jo}(n) = A_{Ja}(n)[/tex]

[tex]48 + 24n = 30n[/tex]

[tex]6n = 48[/tex]

[tex]n = \frac{48}{6}[/tex]

[tex]n = 8[/tex]

They earn the same amount after 8 days.

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