SOLUTION: Samantha spent a total of $420 for daily expenses during her vacation in Mexico. She noted that if she spent $7 less per day, she could have stayed for another 5 days. The number o

Question 941532: Samantha spent a total of $420 for daily expenses during her vacation in Mexico. She noted that if she spent $7 less per day, she could have stayed for another 5 days. The number of days she actually spent on her vacation is:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Samantha spent a total of $420 for daily expenses during her vacation in Mexico. She noted that if she spent $7 less per day, she could have stayed for another 5 days. The number of days she actually spent on her vacation is:
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420 = (# of days)*(cost per day)
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(cost per day-7)(days + 5) = 420
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Simplify::
d*c = 420
(c-7)(d+5) = 420
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cd + 5c - 7d - 35 = 420
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420 + 5c - 7d - 35 = 420
5c - 7d = 35
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Substitute for "c" and solve for "d"::
c = 420/d =
5(420/d) - 7d = 35
2100 - 7d^2 = 35d
d^2 + 5d - 300 = 0
Positive solution::
d = 15 days
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Cheers,
Stan H.
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