SOLUTION: Lee spent $1200 on holiday.Iff he had spent $50 less per day,he could have stayed an extra two days.How long was his holiday?

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Question 1146604: Lee spent $1200 on holiday.Iff he had spent $50 less per day,he could have stayed an extra two days.How long was his holiday?
Found 3 solutions by richwmiller, MathTherapy, greenestamps:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Oops I messed up.
But my wrong answer while showing my work is still better than the "correct" answer and not showing any work at all.


Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
Lee spent $1200 on holiday.Iff he had spent $50 less per day,he could have stayed an extra two days.How long was his holiday?
The other person who responded is WRONG!!

Correct answer: highlight_green%28matrix%281%2C2%2C+6%2C+days%29%29

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Let x be the actual number of days of the vacation. Then

1200/x = daily amount spent
1200/(x+2) = daily amount spent if the vacation were 2 days longer

The amount spent per day would have been $50 less if the vacation had been 2 days longer:

1200%2F%28x%2B2%29+=+1200%2Fx-50

Divide by the common factor of 50 to make the numbers smaller that you have to work with:

24%2F%28x%2B2%29+=+24%2Fx-1

Multiply by the least common denominator, (x)(x+2):

24x+=+24%28x%2B2%29-x%28x%2B2%29
24x+=+24x%2B48-x%5E2-2x
x%5E2%2B2x-48+=+0
%28x%2B8%29%28x-6%29+=+0
x+=+-8 or x+=+6

Clearly the negative value makes no sense in the problem, so

ANSWER: the vacation lasted x=6 days

CHECK:
1200/6 = 200
1200/8 = 150
200-150 = 50