## Wednesday, March 18, 2009

### Shop till you drop

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

Anonymous said...

\$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.

Maria said...

This was fast!
May I allow myself an attempt to simplify your description:
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.