Question

Faith is working two summer jobs, making $13 per hour lifeguarding and $12 per hour washing cars. Last week Faith worked a total of 12 hours and earned a total of $150. Write a system of equations that could be used to determine the number of hours Faith worked lifeguarding last week (x) and the number of hours she worked washing cars last week (y).

Answer 1

if she worked "x" hours lifeguarding at $13 per hour, that means she earned a total of 13*x or 13x, if she worked washing cars for "y" hours at $12 per hour that means she made on those hours 12*y or 12y, and we know that whatever their sum combined is a grand total of $150.

Last week she worked a total of 12 hours doing both, namely x + y = 12.

`\begin{cases} 13x+12y &= 150\\ x + y &= 12 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 2nd equation}}{x +y = 12}\implies y = 12 -x \\\\\\ \stackrel{\textit{substituting on the 1st equation}}{13x+12(12-x) = 150}\implies 13x+144-12x = 150\implies x + 144 = 150 \\\\\\ \boxed{x = 6}~\hfill \stackrel{\textit{we know that}}{y = 12 -x}\implies \boxed{y = 6}`