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.
