# Problem Solving

## CONTENTS OF CURRICULUM UNIT 80.07.07

## Solving Problems “by the Hundreds” A Study of Percentage and Its Applications in the Study of Consumer Related Problems

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## Discount

The amount that an article is reduced in price is called a discount. The rate of discount is the rate of percent that is taken off the original price of the article. The original price of an article is known as the list price or marked price, while the amount for which the article sells after the discount has been subtracted is the net price or sale price.

To find the net price of an item which is being sold at a discount, first multiply the rate of discount by the marked price to obtain the discount, then subtract the discount from the marked price to obtain the net price. To find the rate of discount, divide the discount by the list price and multiply the result by one hundred.

Example 1: | Janet bought a coat which usually sells for $98.00 at 25% off. What did she pay for the coat? | ||

Solution: | 25/100 x $98.00 = 1/4 x 98.00 = $24.50 | discount | |

$98.00 $24.50 =$73.50 | net price | ||

Janet paid $73.50 for the coat. | |||

Example 2: | A blouse marked $10.00 was on sale for $6.00. | ||

Find the rate of discount. | |||

Solution: | $10.00 $6.00 = $4.00 | ||

4/10 x 100/1 = 400/10 = 40% | |||

The rate of discount is 40%. |

Example: | The list price of a lawn mower is $189.95. What is the net price if discounts of 20% and 10% are allowed? |

Solution: | 20/100 x $189.95/1 = 3799/100 = $37.99 |

$189.95 $37.99 = $151.96 | |

10/100 x $151.96/1 = 1519.6/100 = 15.196 = $15.20 | |

$151.96 $15.20 = $136.76 | |

The net price of the lawn mower is $136.76. |

- 1. During a post holiday sale, a department store advertised 40% off all merchandise. What was the sale price of a sofa that originally cost $395?
- 2. A factory outlet offers 20% to 50% reductions on sweaters. If a sweater marked $18 sells for $11.70, what is the rate of discount?
- 3. During the month of February, a retailer is selling electric typewriters at a 10% discount. On Washington’s birthday he is offering an additional 22% off the reduced price. What is the sale price of a typewriter with both discounts if the price was $299.99 before the February sale?
- 4. John paid $6.31 for a book marked 25% off the regular price. What was the regular price of the book?
- 5. On Tuesday the five and ten cent store offers a ten percent discount to senior citizens. With the discount what was the price of the following items? 2 spools of thread .33 each, 4 washcloths .59 each, 1 lb. candy $1.29 lb., 2 sheets $2.99 each.
- 6. One store was offering a 15% discount on all dresses. Another store reduced the prices of all dresses by five dollars. Which was the better buy on a dress marked $25? How much better was it?