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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

$1000

. What was the rate charged per hour by each mechanic if the sum of the two rates was

$155

per hour?

Verified Answer :

naǫ

x - the rate charged by the first mechanic
y - the rate charged by the second mechanic

The sum of the two rates was $155.
@@MATH_TOKEN_0@@

The first mechanic worked for 10 hours, the second mechanic worked for 5 hours, and together they charged $1000.
\(10x+5y=1000 \ \ |\div 5 \\ 2x+y=200 \\ y=200-2x\)

Set 155-x and 200-2x equal to each other:
\(155-x=200-2x \\ -x+2x=200-155 \\ x=45 \\ \\ y=155-x=155-45=110\)

The rate charged by the first mechanic was $45, and the rate charged by the second mechanic was $110.

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