Question

Mike repairs televisions. his revenue, in dollars, can be modeled by the equation y = 25 30x, where x is the number of hours spent repairing televisions. his overhead cost, in dollars, can be modeled by the equation y=5x2−10, where x is the number of hours spent repairing televisions. after how many hours does he break even?

Answer 1

The number of hours spent repairing televisions. after how many hours does he break even is 7 hours

System of equations

These are equations that contains several equations with unknowns. Given the function that modelled the revenue generated from television repair as;

y = 25 + 30x

where:

x is the number of hours spent repairing televisions.

If his overhead cost, in dollars, is modelled by the equation y=5x^2−10, the company breaks even when;

25 + 30x = 5x^2 -10

Divide through by 5

5 + 6x = x^2 - 2

Equate to zero to have:

x^2 - 6x  -2 - 5 = 0

x^2 - 6x - 7 = 0

x^2 - 7x + x - 7 = 0
x(x-7)+1(x-7) =0

x = -1 and 7

Hence the number of hours spent repairing televisions. after how many hours does he break even is 7 hours

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