Abicycle shop designs a new gear system for their bikes. they use a 4-inch gear for 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?

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.

angles 1 and 3 are vertical angles, meaning that they are equal to each other. to solve this you may set angle 1 and 3 equal to each other and just solve for x like

110 = 2x + 10

100 = 2x

50 = x

check:

110 = 2* 50 + 10

110 = 100 + 10

110 = 110

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