Oct 29, 10:22:04 PMJuan is working two summer jobs, making $12 per hour babysitting and making $16per hour lifeguarding. In a given week, he can work at most 17 total hours and mustearn at least $240. If Juan worked 3 hours babysitting, determine all possible valuesfor the number of whole hours lifeguarding that he must work to meet hisrequirements.

Answer:He must need to work 13 hours or 14 hours for lifeguarding.Step-by-step explanation:Consider the provided information.Let x represents the number of hours for babysitting.y represents the number of hours for life-guarding.In a given week, he can work at most 17 total hours and must[tex]x+y\leq 17[/tex]Juan is working two summer jobs, making $12 per hour babysitting and making $16  per hour lifeguarding. He must  earn at least $240.[tex]12x+16y\geq 240[/tex]If Juan worked 3 hours babysitting, Substitute x=3 in [tex]x+y\leq 17[/tex][tex]3+y\leq 17[/tex][tex]y\leq 14[/tex]Thus, he can work at most 14 hours for lifegurading. Substitute x=3 in [tex]12x+16y\geq 240[/tex][tex]12(3)+16y\geq 240[/tex][tex]36+16y\geq 240[/tex][tex]16y\geq 204[/tex][tex]y\geq 12.75[/tex]Therefore, he must need to work 13 hours or 14 hours for lifeguarding.