Question

When two gears are mashed, the revolutions per minute (rpm) are inversely proportional to the number of teeth, as shown below. In one machine the rpm ratio of the large gear to the small gear is 5:7. The small gear has 260 teeth. In a second machine the large gear revolves at 300rpm and has 245 teeth. The small gear revolves at 700rpm.
rpm of large gear=number of teeth on small gear
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rpm of small gear=number of teeth on large gear

Find the number of teeth on the large gear of the first machine.

Find the number of teeth on the small gear

Answer 1

In this first question we get:
\[\frac{5}{7}=\frac{260}{L}\]
L=364 teeth

Answer 2

Question 2:\[\frac{3}{7}=\frac{s}{245}\]
s=105 teeth