Faith is working two summer jobs, making $13 per hour lifeguarding and $12 per hour washing cars. Last week Faith worked a total
of 10 hours and earned a total of $124. Write a system of equations that could be used to determine the number of hours Faith worked lifeguarding last week and the number of hours she worked washing cars last week. Define the variables that you use to write the system
Let's call lifeguarding L and car washing W. In order to write a system, we need to first separate the NUMBER of hours worked from the MONEY earned, because they are very different things.
If she works 10 hours, that is the number of hours worked between both jobs. Therefore, the equation for the NUMBER of hours worked is
L + W = 10.
If she earns $13 an hour lifeguarding, the expression for that is 13L; if she earns $12 an hour car washing, the expression for that is 12W. The MONEY she earned together by doing both those jobs is
