SOLUTION: Jessica has a chance to win $10,000 if she can spend exactly $10089 on 750 boxes of candy, some of which sell for $9 and others that sell for $16 a box. How many boxes of candy doe

Question 668449: Jessica has a chance to win $10,000 if she can spend exactly $10089 on 750 boxes of candy, some of which sell for $9 and others that sell for $16 a box. How many boxes of candy does Jessica choose in order for her to qualify for the $10,000 prize?
Found 2 solutions by DrBeeee, lynnlo:
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
This is the same as a coin problem.
Let a = number of boxes @ $9
Let b = number of boxes @ $16
Then we have
(1) a + b = 750 and
(2) 9*a + 16*b = 10089
Put (1) into (2) and get
(3) 9*(750 - b) + 16*b = 10089 or
(4) 6750 - 9*b + 16*b = 10089 or
(5) 7*b = 3339 or
(6) b = 477 and from (1) we have
(7) a = 273
To check these values use (2).
Is (9*273 + 16*477 = 10089)?
Is (2457 + 7632 = 10089)?
Is (10089 = 10089)? Yes
Answer: Jessica needs to sell 273 of the $9 boxes of candy and 477 of the $16 boxes of candy to get a total sales of $10,089.

Answer by lynnlo(4176) (Show Source): You can put this solution on YOUR website!
273boxes============$9.00========
477boxes============$16.00=======
===================================
750boxes
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