Question

A bicylcle shop designs a new gear system for their bikes.They use a 4-inch gear for the bikes with a 22-inch wheel diameter. If the ratio of the gear to wheel diameter remains constant, what is the size of the gear for a bike with a 26-inch wheel?

Answer 1

Using the principle of constant proportion, the new gear size for a bike with a 26-inch wheel while maintaining the original gear-to-wheel diameter ratio is approximately 4.73 inches.

Step-by-step explanation:

The student asked about the gear size for a bike with a 26-inch wheel if the existing bike uses a 4-inch gear with a 22-inch wheel diameter, and the ratio of the gear size to the wheel diameter is constant.

To find the new gear size, we set up a proportion using the given gear and wheel sizes:

• 4 inches (gear) / 22 inches (wheel) = x inches (new gear size) / 26 inches (new wheel size).

Cross-multiplying to solve for x gives us:

4 inches * 26 inches = 22 inches * x inches

104 = 22x

x = 104 / 22

x = 4.727272... inches

So, the new gear size would be approximately 4.73 inches if we maintain the same ratio for a bike with a 26-inch wheel.

Answer 2

8

4 --

11

Step-by-step explanation:

The gear ratio for the original gear system was 4/22. To get the 22 inch wheel to 26 inches, you have to multiply it by 26/22, so to keep the same ratio, you will also need to multiply 4 by 26/22. You get 104/22, which simplifies to 52/11 which simplified further to 4+8/11. You can check your answer by comparing the original ratio to the new ratio.