\text{Let }b=
Let b=
\,\,\text{the number of hours babysitting}
the number of hours babysitting
\text{Let }l=
Let l=
\,\,\text{the number of hours lifeguarding}
the number of hours lifeguarding
\text{\textquotedblleft at most 17 hours"}\rightarrow \text{17 or fewer hours}
“at most 17 hours"→17 or fewer hours
Use a \le≤ symbol
Therefore the total number of hours worked in both jobs, b+lb+l, must be less than or equal to 17:17:
b+l\le 17
b+l≤17
\text{\textquotedblleft at least \$240"}\rightarrow \text{\$240 or more}
“at least $240"→$240 or more
Use a \ge≥ symbol
Juan makes $12 per hour babysitting, so in bb hours he will make 12b12b dollars. Juan makes $16 per hour lifeguarding, so in ll hours he will make 16l16l dollars. The total amount earned 12b+16l12b+16l must be greater than or equal to \$240:$240:
12b+16l\ge 240
12b+16l≥240
\text{Plug in }\color{green}{3}\text{ for }b\text{ and solve each inequality:}
Plug in 3 for b and solve each inequality:
Juan worked 3 hours babysitting
\begin{aligned}b+l\le 17\hspace{10px}\text{and}\hspace{10px}&12b+16l\ge 240 \\ \color{green}{3}+l\le 17\hspace{10px}\text{and}\hspace{10px}&12\left(\color{green}{3}\right)+16l\ge 240 \\ l\le 14\hspace{10px}\text{and}\hspace{10px}&36+16l\ge 240 \\ \hspace{10px}&16l\ge 204 \\ \hspace{10px}&l\ge 12.75 \\ \end{aligned}
b+l≤17and
3+l≤17and
l≤14and
12b+16l≥240
12(3)+16l≥240
36+16l≥240
16l≥204
l≥12.75
\text{The values of }l\text{ that make BOTH inequalities true are:}
The values of l that make BOTH inequalities true are:
\{13,\ 14\}
{13, 14}
\text{(the final answer is this entire list)}
(the final answer is this entire list)
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