Furnace repairs
A repairman purchased several furnace -blower motors for a total cost of $210. If is cost per motor had been $5 less, he could have purchased one additional motor. How many motors did he buy at the regular rate?
Please help
regular rate = r
discount rate = (r-5)
number bought = n
number that would have been bought = (n+1)
so
210 = r n
and
210 = (r-5)(n+1) = r n + r - 5 n -5
from the first equation r = 210/n
then the second
215 = (210/n)n +210/n -5 n
5 = 210/n -5 n
5 n = 210 -5 n^2
n^2 + n - 42 = 0
(n-8)(n+7)=0
n = 8
sorry
(n+7)(n-6) = 0
n = 6
check
r = 210/n = 35
r-5 = 30
n+1 = 7
30 * 7 = 210 check
thank you very much
HELP!!!!!I need a better explination.
To solve this problem, let's first assign variables to the unknowns.
Let's say the regular cost per motor is 'x' dollars, and the number of motors he bought at the regular rate is 'n'.
According to the given information, the repairman purchased several furnace-blower motors for a total cost of $210. So, the equation for the total cost of the motors becomes:
x * n = 210 ....(Equation 1)
Now, it's given that if the cost per motor had been $5 less, he could have purchased one additional motor. So, the new cost per motor would be (x - 5) dollars, and the number of motors purchased at this reduced rate would be (n + 1).
The new equation for the total cost with the reduced rate becomes:
(x - 5) * (n + 1) = 210 ....(Equation 2)
We now have a system of equations. To find the values of 'x' and 'n', we can solve this system.
Expanding equation 2, we get:
xn + x - 5n - 5 = 210
Rearranging the terms:
xn - 5n + x = 215 ....(Equation 3)
Now, we can solve the system of equations (Equations 1 and 3) to find the values of 'x' and 'n'.
Equation 1: x * n = 210
Equation 3: xn - 5n + x = 215
Substituting xn from equation 1 into equation 3, we get:
210 - 5n + x = 215
Simplifying, we have:
x - 5n = 5 ....(Equation 4)
Now we can solve this new equation (Equation 4) along with Equation 1 using the method of substitution.
Rearranging Equation 4 to solve for x, we have:
x = 5n + 5
Substituting this value of x in Equation 1, we get:
(5n + 5) * n = 210
Expanding, we have:
5n^2 + 5n = 210
Rearranging to make it a quadratic equation:
5n^2 + 5n - 210 = 0
To solve this quadratic equation, you can apply the factoring method, completing the square method, or use the quadratic formula.
Once you find the values of 'n', you can substitute it back into either equation 1 or equation 4 to find the value of 'x', which represents the regular cost per motor.