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?

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