Please help me solve this problem?

The first mechanic worked 10 hours and the second mechanic worked 5 hours. Together they both charged a total of $1250 for their work. Their sum of two rates is $165 per hour. So how much did the first and second mechanics charged?

Please I need help

rate charged by first mechanic --- x

rate charged by second mechanic -- y

"sum of their rates is 165" ---> x+y = 165

"first mechanic worked 10 hours" ---> 10x
"the second mechanic worked 5 hours" --- 5y

"Together they both charged a total of $1250 for their work." ---> 10x+5y=1250

See how I translated the English into Math ?

simplify the 2nd:
10x+5y=1250 , divide each term by 5
2x+y=250

2x+y=250
x+y=165
subtract them:
x = 85
back into the first
85+y=165
y=80

State the conclusion in sentence form.

OK so I just multiplied 85*10 which gave me 850 and 80*5 which gave me 400 and just added it together and got 1250. Thank you!!!

To solve this problem, we need to set up a system of equations.

Let's assume the first mechanic charges $x per hour and the second mechanic charges $y per hour.

From the given information, we can set up the following equations:

Equation 1: 10x + 5y = 1250 (the total amount charged by both mechanics)
Equation 2: x + y = 165 (the sum of their rates per hour)

To solve this system of equations, we can do either substitution or elimination.

Let's use the substitution method to solve for x and y:

First, solve Equation 2 for x:
x = 165 - y

Substitute this value of x into Equation 1:
10(165 - y) + 5y = 1250

Simplify and solve for y:
1650 - 10y + 5y = 1250
-5y = 1250 - 1650
-5y = -400
y = -400 / -5
y = 80

Now that we have the value of y, substitute it back into Equation 2 to solve for x:
x + 80 = 165
x = 165 - 80
x = 85

Therefore, the first mechanic charged $85 per hour, and the second mechanic charged $80 per hour.