Two mechanics worked on a car. the first mechanic worked for 10 hours, and the second mechanic worked for 5 hours. together they charged a total of $1225 . what was the rate charged per hour by each mechanic if the sum of the two rates was $180 per hour?

You would first make an equation to show their individual price per hour multiplied by hours worked then added together to equal total cost. let X be mechanic 1 and Y be mechanic 2

10x + 5y = 1225

the second equation will use their price per hour added together to equal combined cost per hour

x + y = 180

you would solve by substitution. to do so, isolate either x or y in the second equation. for convenience, I will isolate x

x = 180 - y

plug in (180 - y) for x in the first equation

10(180-y) + 5y = 1225

1800 - 10y + 5y = 1225

-5y = -578

y = 115.6

this means that the second mechanic charges $115.60 per hour

to find the price per hour for the first mechanic, plug in (115.6) for y in the second equation

x + 115.6 = 180
x = 64.4

the first mechanic charges $64.40 an hour

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