# 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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## Commission

Sometimes a salesman receives a graduated commission. This means that the rate of commission increases as the amount of sales increases. For example, the rate of commission may be 8% on all sales up to $10,000 and 10% on all sales over $10,000. In many cases a salesman receives a fixed salary plus a commission.

Example 1: | A salesman who works on a commission basis receives 12% of his sales. How much was his commission on a sale amounting to $265? | |

Solution: | Find 12% of $265. | |

Let N= the missing number. | ||

Change 12% to 12/100. | ||

Let “of” denote multiplication. | ||

12/100 x 265/1= N | ||

3180/100= N | ||

N = $31.80 | ||

The salesman earned $31.80 commission. | ||

Example 2: | A salesclerk receives a weekly salary of $120 plus a commission of 5% on all sales above $500 per week. During three weeks her total sales were $1540, $1235, and $1040. What were her total earnings for the three weeks? | |

Solution: | $120 x 3 = $360 | salary for three weeks |

$1540 $500 = $1040 | ||

$1235 $500 = $ 735 | ||

$1040 $500 = $ 540 | ||

$1040 + $735 + $ 540 = $2315 | ||

5/100 x 2315/1 = 11575/100 = $115.75 | commission | |

$360.00 + $115.75 = $475.75 | total earnings | |

Her total earnings were $475.75. |

Solution: | $1300 $800 = $500 | sales above $800 |

8/100 x 800/1 = 6400/100 = $64 | commission | |

14/100 x 500/1 = 7000/100 = $70 | commission | |

$64.00 + $70.00 = $134.00 | total commission | |

His total commission was $134. |

2. Complete the following table.

- 1. A real estate agent receives a commission of 6% of the selling price of a house. If he sells a house for $135,000 what is his commission? What are the net proceeds?

Selling | Rate of | Amount of | Net |

Price | Commission | Commission | Proceeds |

$87,900 | 5% | ||

$500 | $ 75 | ||

6% | $ 84 | ||

10% | $ 108 | ||

325 | $ 300 | ||

$500 | $1,500 |

- 3. A salesman receives a weekly salary of $160 plus a commission of 4% on all sales above $1800. If his sales for four successive weeks were $2180, $1950, $2472, and $2200, find his total earnings from salary and commission for the four weeks.
- 4. A department store clerk receives 12 1/2% commission on all merchandise sold. Last week she received $52 commission. What were her sales for the week?
- 5. Mary earned a 4% commission on the first $650 of weekly sales, and a 6% commission on all sales over $650. Last week her total sales were $1165. How much commission did she receive?