Two mechanics worked on a car. The first mechanic worked for
5
hours, and the second mechanic worked for
15
hours. Together they charged a total of
$2025
. What was the rate charged per hour by each mechanic if the sum of the two rates was
$205
per hour
f + s = 205
5 f + 15 s = 2025 ... f + 3 s = 405
subtracting equations ... 2 s = 200
Let's call the rate per hour charged by the first mechanic "x", and the rate per hour charged by the second mechanic "y".
We know that the first mechanic worked for 5 hours and the second mechanic worked for 15 hours. To find the total amount charged by the first mechanic, we can multiply the rate (x) by the number of hours (5). Similarly, the total amount charged by the second mechanic can be found by multiplying the rate (y) by the number of hours (15).
So, we have the equations:
5x + 15y = 2025 ... (Equation 1)
x + y = 205 ... (Equation 2)
To solve this system of equations, we can use the method of substitution. Rearranging Equation 2, we have:
x = 205 - y
Substituting this value of x into Equation 1, we get:
5(205 - y) + 15y = 2025
Expanding and simplifying, we have:
1025 - 5y + 15y = 2025
10y = 1000
y = 100
Now that we have the value of y, we can substitute it back into Equation 2 to find the value of x:
x + 100 = 205
x = 105
Therefore, the rate per hour charged by the first mechanic is $105, and the rate per hour charged by the second mechanic is $100.