You celebrate the Spring by heading shopping with your friend and agreeing on a maximum cash amount you can spurge. In the first store - Macy's - you spend half the money. In Nordstrom you spend four fifth of what you had left. In Lord-and-Taylor you spend five sixth of what was left. At that point you have load of shopping bags and only $5 left, just enough to pay for coffee and cake before heading home. How much money you started out with?
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2 comments:
$300.
If X is amount at start, then calculate the total amount spent, add $5, and come back to the total:
(1/2)x + (4/5)(1-0.5x) + (5/6)[(1/2)x + (4/5)(1-0.5x)] + 5 = x
Simplifying:
.01668x = 5
x = $300.
Check:
Macy's = $150
Norstrom = $120
L&T = $25
Total = $295.
This was fast!
May I allow myself an attempt to simplify your description:
X - the amount of money to start with
After Macy's we have 1/2 X
After Nordstrom we have 1/5 x 1/2 X = 1/10 X
After Lord&Taylor we have 1/6 x 1/10 X = 1/60 X
And what we have left is $5.
So 1/60 X = $5
X = $5 x 60 = $300
Great job. New puzzle is coming at midnight.
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