Question

Two mechanics worked on a car. The first mechanic worked for 10
hours, and the second mechanic worked for 15
hours. Together they charged a total of 1825
. What was the rate charged per hour by each mechanic if the sum of the two rates was 160
per hour?

Answer 1

How would you figure this one out ?

Answer 2

You need a variable for each mechanic.

Answer 3

So have \(x\) be the first mechanic's rate, and \(y\) be the second mechanics rate.

Answer 4

`What was the rate charged per hour by each mechanic if the sum of the two rates was 160`
This tells us:\[
x+y=160
\]

Answer 5

`The first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. Together they charged a total of 1825`
This tells us \[
10x+15y = 1825
\]

Answer 6

Now we have a system of equations: \[
\begin{split}
x&+&y&=&160\\
10x&+&15y&=&1825
\end{split}
\]

Answer 7

There are two ways we can solve this. First is elimination.
Notice the coefficients of the \(x\)s. The first equation has \(1x\) and t he second had \(10x\). We multiply both equations by the co efficient of the other. It's similar to getting like terms in a fraction: \[
10x+10y=1600\\
10x+15y = 1825
\]Now we subtract the second equation from the first: \[
-5y = -225
\]

Answer 8

We solve for \(y\) and then plug that number into our old equation in order to solve for \(x\).

Answer 9

The second way to solve this is substitution. In this case we isolate a variable in one of the equations:\[
x+y=160 \implies x = 160-y
\]Then we substitute this into the other equation: \[
10x+15y=1825 \implies 10(160-y) + 15y = 1825\implies 5y=225
\]

Answer 10

Then it follows as it would have with elimination.

Answer 11

okidoke awesome ! is there any formula i could remember for any other problems like this ?

Answer 12

and since 5y=225 you would then divide getting your "y" right? then you would go through the problem and solve for "x"?

Answer 13

hello?

Answer 14

There isn't really a general formula.

Answer 15

Yes, you divide by \(5\) to isolate \(y\).