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A factory packages 4250 boxes of cereal. The number of oat cereal boxes is 715 more than the number of wheat cereal boxes. The number of fruit cereal boxes is 5 times the number of wheat cereal boxes. How many fruit cereal boxes does the factory package.

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thisisbenmanley
o = number of oat cereal, w = number of wheat cereal, f = number of fruit cereal:

o + w + f = 4250
o = w + 715
f = 5w

The second equation tells us the value of o in terms of w, and the third equation tells us the value of f in terms of w, so we can plug in "w + 715" for o and "5w" for f in the first equation:

o + w + f = 4250
(w + 715) + w + (5w) = 4250

Then, add like terms and subtract and divide to isolate the w:

w + 715 + w + 5w = 4250
7w + 715 = 4250                           Subtract 715 on both sides:
7w = 3535                                    Divide by 7 on each side:
w = 505

Now that we have w, we can plug it into the last equation to find f, the number of fruit cereal boxes:

f = 5w
f = 5(505)
f = 2525

Therefore, the factory packages 2525 fruit cereal boxes.
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