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 5:7. The small gear has 215 teeth. In a second machine the large gear revolves at 500 rpm and has 336 teeth. The small gear revolves as at 700 rpm.

__rpm of large gear__ = __number of teeth on small gear_____

= rpm of small gear ____ number of teeth on larger gear____

Find the number of teeth on the larger gear of the first machine _301__

Find the number of teeth on the small gear of the second machine. __240__

Solution:

the number of teeth on the larger gear of the first machine: x

215/x = 5/7

x=301

So the number of teeth on the larger gear of the first machine is 301

the number of teeth on the small gear of the second machine: y

336/y = 700/500

y=240

So the number of teeth on the small gear of the second machine is 240