Given:
A repairman purchased several furnace-blower motors for a total cost of $450.
Let the number of motors = x
And the cost of one motor = y
So,
[tex]xy=450\rightarrow(1)[/tex]If his cost per motor had been $5 less, he could have purchased 1 additional motor
So,
[tex](x+1)(y-5)=450\rightarrow(2)[/tex]Divide equation (2) by equation (1)
[tex]\begin{gathered} \frac{(x+1)(y-5)}{xy}=1 \\ (x+1)(y-5)=xy \\ xy-5x+y-5=xy \\ -5x+y-5=0 \\ y=5x+5\rightarrow(3) \end{gathered}[/tex]substitute with (y) from equation (3) into equation (1) then solve for x
[tex]\begin{gathered} x(5x+5)=450 \\ 5x^2+5x=450\rightarrow(\div5) \\ x^2+x=90 \\ x^2+x-90=0 \\ (x+10)(x-9)=0 \\ x+10=0\rightarrow x=-10 \\ x-9=0\rightarrow x=9 \end{gathered}[/tex]The negative result will be rejected
So, x = 9
So, the answer will be:
The number of motors at the regular rate = 9 motors.
And the regular price = $50
