it's been a really long while since i've done anything but basic math. i don't know how to solve this problem and my textbook doesn't give an example at all. I'm hoping someone can help.
Mary and her band receives $550 plus 15% of receipts over $550 for playing a gig. If a club charges a $6 cover charge, how many people must attend in order for Mary and her band to receive $1200?
kohane, here's one approach for progressing from a verbal rendering of the situation, to the algebraic inequality earboth gave you...
The question can be though of as, How many tonedeaf (I've heard Mary's band) people must attend, so that
One at a time, and letting x denote the number of listeners, sticking with earboth's notation...
- The amount that the band will receive, based on the agreement,
- will be at least
Stringing the three components together, the question can thus be expressed as
- The amount the band will receive, at 6 bucks a head, is 550 + 0.15(6x - 550)
- "will be at least" can be rendered as "greater than or equal to", aka
- 1,200 is, well, 1,200
550 + 0.15(6x - 550) 1,200
...and then solving for x will get you to earboth's solution. I hope that helped a bit. Best of luck.