Question

A school store sells jackets for $50, hooded sweat shirts for $30, and shirts for $15. Last month the total revenue from the school clothing was $7800. They sold 360 pieces of clothing. The school store sold 8 times as many shirts as jackets. How many of each type of clothing were sold?

Answer 1

30 Jackets

90 Hooded Sweat Shirts

240 Shirts

Explanation:

Given

Represent each item with their first letters;

`J +H + S = 360`

`50J + 30H + 15S = 7800`

`S= 8J`

Required

Get the value of J, H and S

Substitute 8J for S in the first two equations

`J + H + 8J = 360`

`H + 9J = 360` --- Make H the subject

`H = 360 - 9J`

`50J + 30H +15*8J = 7800`

`50J + 30H +120J = 7800`

`170J + 30H = 7800`

Divide through by 10

`17J + 3H = 780`

Substitute
`H = 360 - 9J`

`17J + 3(360 -9J) = 780`

`17J + 1080 -27J = 780`

Collect Like Terms

`17J -27J = 780 - 1080`

`-10J = -300`

Solve for J

`J = (-300)/(-10)`

`J = 30`

Recall that:
`H = 360 - 9J`

`H = 360 - 9 * 30`

`H = 360 - 270`

`H = 90`

Substitute values for H and J in
`J +H + S = 360`

`30 + 90 + S=360`

`S = 360 - 30 - 90`

`S = 240`