A repairman purchased several furnace-blower motors for a total cost of $150. If his cost per motor had been $5 less, he could have purchased 1 additional motor. How many motors did he buy at the regular rate?
For x motors, $150, so each cost 150/x
For a cost of 150/x - 5, then there were x+1 motors, all for the same $150:
(x+1)(150/x - 5) = 150
x = 5
check:
5 @ $30 = 150
6 @ $25 = 150
Let's denote the number of motors the repairman bought at the regular rate as 'x'.
Using this information, we can set up two equations:
1) The total cost equation: The total cost of the motors purchased is $150. So, the equation becomes:
x * (regular rate) = $150
2) The cost per motor equation: If the cost per motor had been $5 less, the total cost would now be ($150 + cost per motor), and the number of motors purchased would be (x + 1). So, the equation becomes:
(x + 1) * (regular rate - $5) = $150
We can solve this system of equations to find the value of 'x', which represents the number of motors the repairman bought at the regular rate.
Let's solve it step by step:
1) Expand the second equation:
(x + 1) * (regular rate) - (x + 1) * $5 = $150
2) Divide through by the regular rate to simplify the equation:
(x + 1) - 5 = $150 / (regular rate)
3) Simplify further:
x - 4 = $150 / (regular rate)
4) Multiply through by (regular rate) to bring the regular rate back into the equation:
x * (regular rate) - 4 * (regular rate) = $150
5) Substitute the first equation into this equation:
$150 - 4 * (regular rate) = $150
6) Simplify:
- 4 * (regular rate) = 0
7) Divide through by -4:
(regular rate) = 0
From this equation, we can conclude that the regular rate is $0, which doesn't make sense. Therefore, there seems to be an error in the problem statement or some missing information.