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

Algebra ->  Customizable Word Problem Solvers  -> Misc -> 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      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

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) About Me  (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:
-----
420 = (# of days)*(cost per day)
------
(cost per day-7)(days + 5) = 420
===============================
Simplify::
d*c = 420
(c-7)(d+5) = 420
------
cd + 5c - 7d - 35 = 420
----
420 + 5c - 7d - 35 = 420
5c - 7d = 35
---
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
---------------------
Cheers,
Stan H.
===============