Q:

Your sister is getting married this summer and she has asked you to help her select a D.J.for the big event. You called around and found the Dave the D.J. charges a $150.00 set upfee, plus $10.50 per hour. You discover Marvin’s Mobile Music Machine has a $135.00 setup fee, plus $15.00 per hour. Problem solve with your group to determine which D.J. willyou recommend to your sister? Write a letter to your sister to your sister which D.J to recommend. a >>letter<

Accepted Solution

A:
so Dave charges 150 at first and then 10.50 per each hour, so if your sister has the party going for say "h" hours, then his total charges will then be 150 + 10.5h.

now, Marvin's Mobile Music charges 135 at first, but then is more expensive per hour is 15 bucks per each hour, so if she has a party for "h" hours, then his total charges are 135 + 15h.

now, let's check when they're both equal, at how many hours will they cost your sister the same amount.

[tex]\bf 150+10.50h=135+15h\implies 150-135=15h-10.5h \\\\\\ 15=4.5h\implies 15=4\frac{1}{2}h\implies 15=\cfrac{9}{2}h\implies \cfrac{15}{\frac{9}{2}}=h\implies \cfrac{\frac{15}{1}}{\frac{9}{2}}=h \\\\\\ \cfrac{15}{1}\cdot \cfrac{2}{9}=h\implies \cfrac{30}{9}=h\implies \cfrac{10}{3}=h\implies 3\frac{1}{3}=h[/tex]

so, 3 and a third of a hour, or 3 hours and 20 minutes, they both will cost your sister the same amount, so it wouldn't matter who's hired if the party is only 3 hours and 20 minutes long.

however, after that, the one with higher hourly rate, Marvin's, gets more expensive, and she's better off hiring the one with cheaper hourly rate.

now, you can just get some mp3s and some loud speakers and nevermind the  DJs and you do it, or she can do it, I have the macarena song if you need that one.