Question

2. Kylie wants to earn $100 a month. She rakes leaves for $7 an hour and cleans windows for $6 an hour. Kylie cannot work more than 30 hours a week. Write the system of inequalities that represents this situation. Be sure to define your variables.

Answer 1

Let L be the amount of hours that Kylie works on raking leaves and W the amount of hours that she works on cleaning windows (on a week).

Since she cannot work more than 30 hours a week, and the total time spent working is L+W, then:

$L+W<30$

Since one month has 4 weeks, she should win $25 a week to earn $100 in a month. Since she gets paid $7 per hour for raking leaves, after L hours she would have won a total amount of 7L, and since she gets paid $6 for cleaning windows, she would have won 6W after W hours. The total amount of money earned would be 7L+6W, which should be greater than 25:

$25\le7L+6W$

Therefore, the system of inequalities that represents the situation, is:

$\begin{gathered} L+W\le30 \\ 25\le7L+6W \end{gathered}$