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?

If the amount of $1.50 wrenches he buys is x, then 1.5x is the amount he pays for $1.50 wrenches since he pays another $1.50 for each wrench he buys of that cost. In addition he buys x amount of $2.50 wrenches, x/2 of 4$ wrenches (since x/2= half of x), and (x/2)+1 is the amount of 3$ wrenches. Adding them all up, we get 1.5x+2.5x+4(x/2)+3(x/2+1)=total cost=78. Since 4/2=2 and 3/2=1.5, we can add these up to get 4x+2x+1.5x+3=7.5x+3=78. Subtracting 3 from both sides, we get 7.5x=75 and by dividing both sides by 7.5, we get x=10. Therefore, Mr. Abernathy buys 10 $1.50 wrenches, 10 $2.50 wrenches, 10/2=5 $4 wrenches, and 5+1=6 3$ wrenches