# You make a purchase at Johnson's Discount Mart. When you take your items to the cashier, there first is a 25% discount because of the store-wide sale in effect. Then the cashier says you're spending enough to warrant an additional 10% discount. When you're ready to pay you pull out cash instead of a credit card and this gets you another discount of 3%. You pay \$195.89. We'll pretend there's no tax on top of this amount. How much would you have paid without any discounts? Hint: the discounts are successive, not additive so the total discount is not 38%. Your total bill is \$195.89 after receiving discounts of 25%, 10%, and 3% successively and we are asked to find the bill without discounts.

Let x be the original total bill. Then the amount paid can be found:

(.75)(.9)(.97)x=195.89

** If there is a 25% discount then the amount due is 75% of the original price thus multiply by .75. Similarly a 10% discount is 90% and a 3% discount is .97 of the cost. We apply them in succession -- the total bill then apply a 25% discount, then apply a 10% discount to the subtotal and finally apply a discount to that subtotal. **

Dividing both sides of the equation by (.75)(.9)(.97)=.65475 we get x is approximately 299.18.

Thus the nondiscounted bill would have been \$299.18

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