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 woYou 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?uld be the diameters of the coins in your set?
Answers
Given:
All coins will be circular and coloured silver, but of different diameters.
To find:
You are asked to design a new set of coins.
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.
Solution:
As 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.
⇒ The dameters of coins range from 15 mm to 45 mm.
• given a coin, the diameter of the next coin must be at least 30% larger.
15 mm × 30% = 4.5 ⇒ 15 + 4.5 = 19.5 mm ≈ 20 mm
20 mm × 30% = 6 ⇒ 20 + 6 = 26 mm
26 mm × 30% = 7.8 ⇒ 26 + 7.8 = 33.8 mm ≈ 34 mm
34 mm × 30% = 10.2 ⇒ 34 + 10.2 = 44.2 mm ≈ 45 mm
• 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).
19.5 mm ≈ 20 mm
25.35 mm ≈ 26 mm
33.8 mm ≈ 34 mm
44.2 mm ≈ 45 mm
∴ 15 – 20 – 26 – 34 – 45 are the dimeters of the coins.
Step-by-step explanation:
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