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

Answer:

30 Jackets

90 Hooded Sweat Shirts

240 Shirts

Step-by-step 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

$J = \frac{-300}{-10}$

$J = 30$

Recall that: $H = 360 - 9J$

$H = 360 - 9 * 30$

$H = 360 - 270$

$H = 90$

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

$30 + 90 + S=360$

$S = 360 - 30 - 90$

$S = 240$