Question

Mustafa and Diego both work as plumbers. Mustafa charges $150 to make a service call plus $50 per hour. Diego charges $50 to make a service call plus $75 per hour.a) Write an equation to represent the cost (C) of hiring Mustafa for n hours.b) Write an equation to represent the cost (C) of hiring Diego for n hours.c) Today, they both worked the same number of hours and earned the same amount of money. How many hours did they work?

Answer 1

Solution:

Given that;

Where, C is the cost of hiring a plumber and n represents hours worked

Mustafa and Diego both work as plumbers

a) Mustafa charges $150 to make a service call plus $50 per hour,

The equation representing the cost (C) of hiring Mustafa for n hours will be

$C=150+50n$

Hence, the answer is

$C=150+50n$

b) Diego charges $50 to make a service call plus $75 per hour,

The equation representing the cost (C) of hiring Diego for n hours will be

$C=50+75n$

Hence, the answer is

$C=50+75n$

c) Today, they both worked the same number of hours and earned the same amount of money, then,

$\begin{gathered} 150+50n=50+75n \\ \mathrm{Subtract\:}150\mathrm{\:from\:both\:sides} \\ 150+50n-150=50+75n-150 \\ 50n=75n-100 \\ Collect\text{ like terms} \\ 75n-50n=100 \\ 25n=100 \\ n=\frac{100}{25} \\ n=4 \end{gathered}$

Hence, they worked for 4 hours