Disclaimer: This Mathematics question is purely created for discussion purpose. Any resemblance to actual questions from books or schools is coincidental.

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Q: A restaurant manager engages a mover to move 800 imported wine glasses from the port to the restaurant. For wine glasses that have safely reached the restaurant, the manager pays $0.60 each. But, if the wine glasses are broken, the mover has to pay $6.80 each to the manager as a compensation.

If the mover receives $450.40 as the payment, how many wine glasses have safely reached the restaurant?

A: At first glance, many students first find the payment for all 800 wine glasses safely reached the restaurant.

Payment for 800 wine glasses = 800 x $0.60 = $480

Subsequently, they will find how many are broken by subtracting and dividing,

$480 – $450.40 = $29.60

Here, they face a problem because $29.60 ÷ $6.80 = 4.35. There is a remainder and they start to doubt whether the question is written correctly.

The question is written correctly. Below are two methods to solve the problem. The first is using table, which is easy to understand. The second is using algebra.

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1. From the table below, the answer is 796 wine glasses have safely reached the restaurant.

Quantity of wine glasses safely reached the restaurant |
Quantity of broken wine glass(es) |
Total Payment |

800 |
0 |
800 x $0.60 – 0 = $480 |

799 |
1 |
799 x $0.60 – 1 x $6.80 = $472.60 |

798 |
2 |
798 x $0.60 – 2 x $6.80 = $465.20 |

797 |
3 |
797 x $0.60 – 3 x $6.80 = $457.80 |

796 |
4 |
796 x $0.60 – 4 x $6.80 = $450.40 |

2. From the table above, we can write the algebraic equation to represent the problem.

a = quantity of wine glasses safely reached the restaurant

p = payment

p = a(0.6)-(800-a)(6.8)

Simplify the equation, p = 0.6a – 800(6.8) + 6.8a

p = 7.4a – 5440

Solve the equation, 450.4 = 7.4a – 5440

and you get a = 796.

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Pros and cons of the above two methods

Method 1: Pro — Simple step to solve a seemingly complicated question.

Con — It is time-consuming if the quantity of wine glasses safely reached the restaurant is smaller, you need to continue the list until you find the answer.

Method 2: Pro — Fast and can find the answer easily even if the quantity of wine glasses safely reached the restaurant changes.

Con — The first step to find the algebraic equation is the key, if the equation is wrong, it will lead to wrong answer. For students who are weak in algebra, they may spend longer time to find the correct algebraic equation.