Two mechanics worked on a car. The first mechanic worked for 10 hours and the second mechanic worked for 15 hours. Together they charged $2500. What was the rate charged per hour by each mechanic if the sum of the two rates was $195 per hour?
10 x + 15 y = 2500
y = 195-x
10 x + 15(195-x) = 2500
10 x + 2925 - 15 x = 2500
5 x = 425
x = 85
y = 195-x = 110
To find the rate charged per hour by each mechanic, let's assume the rate charged by the first mechanic is "x" dollars per hour, and the rate charged by the second mechanic is "y" dollars per hour.
We know that the first mechanic worked for 10 hours, so the first mechanic would have charged 10x dollars for their work.
Similarly, the second mechanic worked for 15 hours, so the second mechanic would have charged 15y dollars for their work.
Together, the two mechanics charged a total of $2500, so we can write the equation: 10x + 15y = 2500.
We're also given that the sum of the two rates was $195 per hour, so we can write the second equation: x + y = 195.
Now, we have a system of two equations with two unknowns. We can solve this system using substitution or elimination.
Let's use elimination to solve the system:
From the second equation, we can rewrite it as x = 195 - y.
Substituting this expression for x in the first equation, we have: 10(195 - y) + 15y = 2500
Expanding: 1950 - 10y + 15y = 2500
Combining like terms: 5y = 550
Dividing both sides by 5: y = 110
Now, we substitute the value of y back into the expression for x: x = 195 - 110 = 85
Therefore, the rate charged per hour by the first mechanic (x) is $85, and the rate charged per hour by the second mechanic (y) is $110.