Question

Mr. Abernathy purchases a selection of wrenches for his shop. His bill was $78. He buys the same number of $1.50 and $2.50 wrenches, and half that many $4 wrenches. The number of $3 wrenches is one more than the number of $4 wrenches. How many of each did he purchase?

Answer 1

He purchased 10 $1.50 and 10 $2.50 wrenches. And 5 $4 wrenches and 6 $3 wrenches.

Explanation:

Lets represent the number of $1.50 wrenches by x

The number of $1.50 and $2.50 wrenches are equal. The number of $4 wrenches is x/2 since its half of number of $1.50 wrenches and the number of $3 wrenches is (x/2) +1. So the equation is

x(1.50) + x(2.50) + x/2(4) + ((x/2)+1)(3)=78

1.5x+2.5x+2x+(3x/2)+3=78

6x+(3x/2)=78-3

6x+(3x/2)=75

Multiply through by the LCM

12x+3x=150

15x=150

15x/15=150/15

x=10

Since the number of $1.50 wrenches is x, the number of $1.50 wrenches is 10.

The same applies to $2.50.

$4 is x/2 which is 10/2=5

$3 is (x/2) +1 and x/2 is 10/2 which is 5

so it 5+1=6