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?

Like shopping? Try this story from TheMathMom: Shopping Math Or, How To Convince Yourself Into Buying Anything You Want

## 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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