Question

A school band ordered hats for 3 dollars and large shirts for 5 dollars. They bought 150 items in all for 590 dollars. Graph a system of equations to find how many hats and shirts the band ordered.

Answer 1

The number of hats ordered is 80 and the number of shirts ordered is 70.

Explanation:

Given that :

• Cost of hats = $3
• Cost of shirts = $5

The total cost of all the items = $590.

The total number of items bought = 150 items.

Let us assume :

• The number of hats ordered = x
• The number of shirts ordered = y

The equation can formed as :

x+y = 150 ---------(1)

3x+5y = 590 ------------(2)

Multiply eq(1) by 3 and subtract eq(2) from eq(1),

3x+3y = 450

-(3x+5y = 590)

-2y = - 140

2y = 140

y = 140/2

y = 70.

The number of shirts ordered is 70.

Substitute y=70 in eq(1),

x+70 = 150

x = 150-70

x = 80.

The number of hats ordered is 80.