Question

The owner of a discount clothing store ordered six belts and eight hats for $140. A

week later, at the same prices, he bought nine belts and six hats for $132. Find the
price of a belt and a hat.

Answer 1

Let b = the price of the belt
h = the price of the hat
Equation 1
6b + 8h = 140
Equation 2
9b + 6h = 132
Multiply equation 1 by 1.5
1.5(6b + 8h = 140)
9b +12h = 210
Subtract by equation 2
9b-9b +12h-6h = 210-132
6h = 78
h = 13
Substitute h = 13 in equation 1
6b + 8*13 = 140
6b = 140 - 104
6b = 36
b = 6
The price of the hat is $13.00 each
The price of the belt is $6.00 each