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?
x - the rate charged by the first mechanic y - the rate charged by the second mechanic
The sum of the two rates was $155. [tex]x+y=155 \\
y=155-x[/tex]
The first mechanic worked for 10 hours, the second mechanic worked for 5 hours, and together they charged $1000. [tex]10x+5y=1000 \ \ |\div 5 \\
2x+y=200 \\
y=200-2x[/tex]
Set 155-x and 200-2x equal to each other: [tex]155-x=200-2x \\
-x+2x=200-155 \\
x=45 \\ \\
y=155-x=155-45=110[/tex]
The rate charged by the first mechanic was $45, and the rate charged by the second mechanic was $110.
