Question

a mechanic worked 20 hours. another mechanic worked 15 hours. together they charged a total of $1950. what was the rate charged per hour for each mechanic if the sum of the two rates were $115 per hour

Answer 1

Answer: The mechanics both charged $70 and $45 per hour respectively

Step-by-step explanation: We shall start by calling the mechanics hourly rates x and y respectively. So if one worked for 20 hours and charged 20 times x dollars, and the other one worked for 15 hours and charged 15 times y dollars, totalling 1950 dollars, we can write the following expression,

20x + 15y = 1950

Also, if the sum of the two rates was 115 dollars, that means for working for an hour only, they both would earn

x + y = 115

We now have a pair of simultaneous equations

20x + 15y = 1950 --------(1)

x + y = 115 ------------------(2)

We shall use the substitution method for this problem.

From equation (2), make x the subject of the equation

x = 115 - y

Substitute for the value of x into equation (1)

20(115 - y) + 15y = 1950

2300 - 20y + 15y = 1950

By collecting like terms we now have

2300 - 1950 = 20y - 15y

(Note that when a negative value crosses to the other side of the equation, it becomes a positive value and vice versa)

350 = 5y

Divide both sides of the equation by 5

70 = y

We now substitute for the value of y into equation (2)

x + y = 115

x + 70 = 115

Subtract 70 from both sides of the equation

x = 45.

Therefore, the rate they charged per hour were $45 and $70 respectively.