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?
This is similar to what I just answered earlier.
x = total cost
y= # of motors bought
150 = x*y
solving for y:
150/y= x <--- (1)
now we know:
150=(x-2)*(1+y) <--- (2)
substitute using (2) and (1) we get :
150=((150/y)-5)*(1+y)
30 = y^2+y
y^2+y -30= 0
(y+6)(y-5)=0
y = -6, 5
real solution is 5, can't buy negative engines..
To solve this problem, let's assume that the repairman initially purchased x motors at the regular rate.
According to the information given, the total cost of all the motors is $150. So, the cost per motor at the regular rate is $150 divided by x, which is $150/x.
If the cost per motor had been $5 less, then it would have been ($150/x) - $5.
The problem states that if the cost per motor had been $5 less, the repairman could have purchased 1 additional motor. This means that the number of motors purchased at the reduced rate is (x + 1).
Now, we can set up an equation based on this information:
x * ($150/x) = (x + 1) * (($150/x) - $5)
We can simplify this equation:
$150 = (x + 1)*($150 - $5x)/x
$150x = (x + 1)*($150 - $5x)
Now, we can solve this equation to find the value of x.
$150x = $150*($150 - $5x) - $5x*($150 - $5x)
$150x = $22500 - $750x - $750x + $25x^2
Rearranging the equation and simplifying further:
$25x^2 - $1500x + $22500 = 0
Dividing the entire equation by $25, we get:
x^2 - 60x + 900 = 0
Now, we can solve this quadratic equation by factoring. The factors of 900 that add up to -60 are -30 and -30. So, the factored form is:
(x - 30)(x - 30) = 0
(x - 30)^2 = 0
Taking the square root of both sides, we get:
x - 30 = 0
x = 30
Therefore, the repairman bought 30 motors at the regular rate.