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### Shopping

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

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/
```
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