Question

Bob, Bill, and Joe measured their heights. They figured out that the height of Bob is equal to b cm and he makes up 8/9 of the height of Bill. The height of Bill makes up 3/32 of the height of Joe. How many times is Joe taller than Bob? Does the answer rely on the meaning of b?

Answer 1

Answer:

Joe is 12 times taller than Bob

No the answer not rely on the meaning of b

Step-by-step explanation:

* Lets explain how the solve the problem

- The height of Bob is equal to b cm

- The height of Bob is 8/9 of the height of Bill

- Because 8/9 is less than one , then Bob is shorter than Bill

- The height of Bill makes up 3/32 of the height of Joe

* Lets write these information by mathematics relation

∵ The height of Bob is b

∵ The height of Bob is 8/9 height of Bill

∴ b = 8/9 the height of Bill

- Multiply both sides by 9

∴ 9 b = 8 the height of Bill

- Divide both sides by 8

∴ 9/8 b = the height of Bill

∴ The height of Bill is 9/8 b

∵ The height of Bill is 3/32 the height of Joe

∴ 9/8 b = 3/32 the height of Joe

- Multiply both sides by 32

∴ 36 b = 3 the height of Joe

- Divide both sides by 3

∴ 12 b = the height of Joe

∴ The height of Joe is 12 b

∵ b is the height of Bob

∴ The height of Joe is 12 times the height of Bob

∴ Joe is 12 times taller than Bob

- NO, the answer doesn't depend on b because the ratio between the

 heights of Joe and Bob doesn't change by the change of b