Shopping

Date: 8/26/96 at 18:48:14
From: Anonymous
Subject: Spending money

Please help me solve the following.  I am completely lost.

A shopper has $62.00 to spend.  Her shopping list includes a $16.95 
purse, a $21.00 shirt, and a $39.50 telephone.  She must pay 6 percent 
sales tax on her purchases.  Which items should she buy if she wants 
to spend as much of the $62.00 as possible? What would the amount be? 
She can buy more than one of the same item.

Date: 8/27/96 at 13:20:49
From: Doctor Robert
Subject: Re: Spending money

If the shopper must pay sales tax of 6 percent, then the maximum 
amount that she can spend (before taxes) can be calculated as follows.  
Let x be the amount she can spend.  Then .06x is the tax.  Then

   x + .06x = 62    or 1.06x = 62.

Dividing by 1.06 we find that x = $58.49.  Now WHAT should she buy?  
You just have to try different combinations, but offhand it seems to 
me that maybe 2 purses and a shirt would be close to the maximum 
since 2 times $16.95 + $21.00 = $54.90.  Check it out!

-Doctor Robert,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/