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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?

Respuesta :

MrRoyal

Answer:

30 Jackets

90 Hooded Sweat Shirts

240 Shirts

Step-by-step explanation:

Given

Represent each item with their first letters;

[tex]J +H + S = 360[/tex]

[tex]50J + 30H + 15S = 7800[/tex]

[tex]S= 8J[/tex]

Required

Get the value of J, H and S

Substitute 8J for S in the first two equations

[tex]J + H + 8J = 360[/tex]

[tex]H + 9J = 360[/tex] --- Make H the subject

[tex]H = 360 - 9J[/tex]

[tex]50J + 30H +15*8J = 7800[/tex]

[tex]50J + 30H +120J = 7800[/tex]

[tex]170J + 30H = 7800[/tex]

Divide through by 10

[tex]17J + 3H = 780[/tex]

Substitute [tex]H = 360 - 9J[/tex]

[tex]17J + 3(360 -9J) = 780[/tex]

[tex]17J + 1080 -27J = 780[/tex]

Collect Like Terms

[tex]17J -27J = 780 - 1080[/tex]

[tex]-10J = -300[/tex]

Solve for J

[tex]J = \frac{-300}{-10}[/tex]

[tex]J = 30[/tex]

Recall that: [tex]H = 360 - 9J[/tex]

[tex]H = 360 - 9 * 30[/tex]

[tex]H = 360 - 270[/tex]

[tex]H = 90[/tex]

Substitute values for H and J in [tex]J +H + S = 360[/tex]

[tex]30 + 90 + S=360[/tex]

[tex]S = 360 - 30 - 90[/tex]

[tex]S = 240[/tex]

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