# 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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## Sales Tax and Gratuities

To compute the amount of sales tax to be added to the purchase price of any item, multiply the rate of percent by the price of the item. The result usually is rounded to the nearest cent. To round any amount of money to the nearest cent, look at the digit to the right of the hundredths place. If this digit is less than five, drop it and keep the cents obtained in the product. If the digit to the right of the hundredths place is five or greater, drop it and add one to the cents obtained in the product.

Example 1: | Round the following to the nearest cent: | |

a) $5.2763 | b) $.6419 | |

Solution: | a) $5.2763 = $5.28 | b) $.6419= $.64 |

Example 2: | Find 7.5% of $495. | |

Solution: | 7.5/ 100 x 495/1 = 3712.5/100 = $37.125 = $37.13 |

Fifteen percent of any amount may be calculated mentally by using the following three steps: (1) Find ten percent of the amount by moving the decimal point one place to the left. (2) Find five percent of the amount by taking one half of the answer in step one. (3) Add the answers in steps one and two.

Example 1: | Calculate 15% of $3.89 mentally. | |

Solution: | 10% of $3.89 = $.389 | |

1/2 of .389 = .1945 | ||

.389 + .1945 =.39 + .19 = .58 | ||

15% of $3.89 is $.58. | ||

Example 2: | Mary bought a purse for $10.95 and a pair of shoes for $18.95. What total amount did she pay if a 7.5% sales tax was added to the price of the items? | |

Solution: | $l0.95 + $l8.95 = $29.90 | Cost of the items |

7.5/100 x 29.90/1 = 224.25/100 = $2.24 Sales Tax | ||

$29.90 + $2.24 = $32.14 Total Paid | ||

Example 3: | Jim had luncheon downtown last week. He ordered a hamburger at $.95, potatoes at $.65, and a coke at $.50. What total amount did he pay if a 7.5% sales tax and a 15% tip were added to the price of the food?: | |

Solution: | .95 + .65 + .50 = $2.10 | Cost of the luncheon |

7.5/100 x 2.10 =$.16 | Sales Tax | |

10% of $2.10 = $.21 | ||

5% of $2.10 = $.105 = $.11 | ||

$. 21 + .11 = $.32 | Tip | |

$2.10 + $.16 + $.32 = $2.58 | Total Paid |

- 1. Using a 7.5% sales tax, find the amount of tax and the total paid for the following items:

Item | Price | Sales Tax | Total Paid |

toothpaste | .69 | ||

greeting card . | 40 | ||

comb | .35 | ||

lemonade | .79 | ||

soap powder | 1.58 |

- 2. During November Mrs. English made the following purchases at a department store.

skirt | $14.95 | stockings | $1.98 |

dress | $45,00 | dusting powder | $2.75 |

blouse | $17.00 | shoes | $24.00 |

MENU

- Find the total amount of the bill including a sales tax of 7.5% on each item.
- 3. Mrs. Green bought the following items at the Orange Market: 6 lb. roast beef $2.39 lb., 2 lb. coffee $3.29 lb., 3 bottles of soda .39 each (taxable item plus 5¢ deposit on each bottle), 8 bars soap 4 bars for .69 (taxable item), 1 bottle shampoo .99 (taxable item), 10 lb. potatoes $1.19. Find the total amount of the purchase including a 7.5% sales tax on taxable items and deposits on bottles.
- 4. Fifteen office workers are planning to go out to dinner. Using the menu below select a dinner for each person. Find the total cost of the bill including a 7.5% sales tax and a 15% tip.

Appetizers

Shrimp Cocktail | $4.55 |

Alaskan King Crab Legs | $4.55 |

Iced Cherrystones on half shell | $3.50 |

Clams Casino | $3.50 |

Baked Stuffed Clams | $3.50 |

Whole Lobster one and onehalf lbs. | $17.34 |

Lobster Tails | $16.25 |

Fisherman’s Platter | $12.45 |

Baked Stuffed Shrimp | $9.95 |

Shrimp Scampi | $9.95 |

Baked Stuffed Sole | $9.95 |

Alaskan King Crab Legs Fra Diavolo | $10.95 |

Scallops with Lobster Sauce | $9.95 |

Broiled Swordfish Steak | $9.95 |

Reef & Beef | $11.95 |

New York Cut Sirloin Steak | $10.75 |

Filet Mignon with Stuffed Tomato | $12.95 |

Prime Rib Au Jus | $9.95 |

Roast Leg of Spring Lamb | $9.95 |