Mr. abernathy bought a selection of wrenches for his shop and paid $78. he bought the same number of $1.50 and $2.50 wrenches, and half of that number of $4 wrenches. the number of $3 wrenches is one more than the number of $4 wrenches. how many of each did he buy?

Let the number of $1.50 wrenches be x,
number of $2.50 wrenches = x
number of $4 wrenches = x/2
number of $3 wrenches = x/2 + 1

amount paid for $1.50 wrenches = 1.5x
amount paid for $2.50 wrenches = 2.5x
amount paid for $4 wrenches = 4(x/2)
= 2x
amount paid for $3 wrenches = 3(x/2 + 1)
= 1.5x + 3

total amount paid = 1.5x + 2.5x + 2x + 1.5x + 3
= 7.5x + 3
7.5x + 3 = 78
7.5x = 75
x = 10

number of $1.50 wrenches = x
= 10
number of $2.50 wrenches = x
= 10
number of $4 wrenches = x/2
= 10/2
= 5
number of $3 wrenches = x/2 + 1
= 10/2 + 1
= 5 + 1
= 6

He bought 10 $1.50 wrenches, 10 $2.50 wrenches, 5 $4 wrenches and 6 $3 wrenches.

Where are the