Question

You are asked to design a new set of coins. All coins will be circular and coloured silver, but of different diameters. Researchers have found out that an ideal coin system meets the following requirements:
• diameters of coins should not be smaller than 15 mm and not be larger than 45 mm.
• given a coin, the diameter of the next coin must be at least 30% larger.
• the minting machinery can only produce coins with diameters of a whole number of millimetres (e.g. 17 mm is allowed, 17.3 mm is not).




Question 1: You are asked to design a set of coins that satisfy the above requirements. You should start with a 15 mm coin and your set should contain as many coins as possible. What would be the diameters of the coins in your set?
With explanation give answer

Answer 1

Given : Circular Coins

diameters of coins should not be smaller than 15 mm and not be larger than 45 mm.

diameters of a whole number of millimetres

diameter of the next coin must be at least 30% larger.

To Find : design a set of coins that satisfy the above requirements.

Solution:

Smallest coin  Diameter =  15 mm

Next coin   Diameter  ≥  15 + (30/100)15

≥ 15 + 4.5

≥ 19.5

Next coin   Diameter = 20 mm

Next coin   Diameter  ≥ 20 + (30/100)20

≥ 20 + 6

≥ 26

Next coin   Diameter = 26 mm

Next coin   Diameter  ≥ 26 + (30/100)26

≥ 26 + 7.8

≥ 33.8

Next coin   Diameter = 34 mm

Next coin   Diameter  ≥ 34 + (30/100)34

≥ 34 + 10.2

≥ 44.2

Next coin   Diameter = 45 mm

Coins Diameters  = 15 mm , 20 mm , 26 mm , 34 mm , 45 mm

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