A machine shop is manufacturing a pair of gears that need to be in a ratio as close to 1.1839323 as possible, but they can't make gears with more than 50 teeth on them. How many teeth should be on each gear to best approximate this ratio?

Question

Camille Orozco

Mathematics

4 December, 13:16

A machine shop is manufacturing a pair of gears that need to be in a ratio as close to 1.1839323 as possible, but they can't make gears with more than 50 teeth on them. How many teeth should be on each gear to best approximate this ratio?

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Answers (1)

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Gavin Valdez · Answer 1

Answer: Driven gear will have 50 teeth, and driver gear will have 42 teeth

Step-by-step explanation: First we have to know the formula of gear ratio which is started below

(No of teeth on driven) / (No of teeth on driver)

Note: we should all know in the combination of a gear system, we have two gears, the driver gear and the driven gear

So since the least amount of teeth for any gear is 50, we assume the no of teeth on the driven is 50

And no of teeth on the driver is x

50/x = 1.1839323

Cross multiply

x x 1.1839323 = 50

x = 50/1.1839323

x = 42.23

To the nearest whole number = 42

So therefore, number of teeth on the driver gear is 42