Question

Susan is looking to hire a cleaning company to clean her house every week. One cleaning company's cost can be calculated by the expression 75 + 50x, where x is the amount of hours they spend cleaning. Another cleaning company's cost can be calculated using the expression 50 + 75x. Susan wants to know how long each company will have to clean to cost the same amount. Group of answer choices 1 hour 2 hours the will never equal the same 7.5 hours

Answer 1

A. 1 hour

Explanation:

If one cleaning company's cost can be calculated by the expression 75 + 50x, where x is the amount of hours they spend cleaning and another cleaning company's cost can be calculated using the expression 50 + 75x, then to calculate how long each company will have to clean to cost the same amount, we will equate both expression of the company cost and solve for x as shown;

On equating:

75 + 50x, = 75x + 50

collect like terms'

50x-75x = 50-75

-25x = -25

divide both sides by -25

-25x/-25 = -25/-25

x = 1

hence the number of hours each company will have to clean to cost the same amount is 1 hour