Question

When two gears are mashed, the revolutions per minute (rpm) are inversely proportional to the number of teeth as shown like this (rpm of large gear)/(rpm of small gear)=(number of teeth on small gear)/(number of teeth on large gear). In one machine the rpm ratio of the large gear to the small gear is 3.5. The small gear has 123 teeth. In a second machine the large gear revolves at 500 rpm and has 238 teeth. The small gear revolves at 700 rpm.
Find the number of teeth in the large gear of the first machine?
And
Find the number of teeth on the small gear of the second machine?

Answer 1

\[3.5=123/x\]

Answer 2

The first problem is rounded off. If the ratio is 3.5=7/2, the smaller gear has to have an even number of teeth.

Answer 3

\[x=35 teeth\]

Answer 4

500/700=x/238

Answer 5

x=170 teeth

Answer 6

a. x = 35 teeth
b. x = 170 teeth

Answer 7

The answer above for the second question is correct. The answer above for part a is in error.

Answer 8

Where is the error?

Answer 9

The setup above was backwards. Correct setup is 3.5=7/2=larger/smaller=x/123. After cross-multiplication, we get an answer with a fractional number of teeth on the gear. Not usually very practical. Either the ratio was rounded off (very possible, and common in real life) or the problem was stated in error.

Answer 10

3.5=7/2=smaller/larger=123/x according to the question.

Answer 11

Explain exactly how a fraction with the smaller number in the numerator is going to be more than one.....

Answer 12

I think you may be right about the problem being written wrong. The ratio stated in the question doesn't make sense.

Answer 13

Thank you for the vote of confidence.

Answer 14

maybe the ratio is supposed to be 3:5 instead of 3.5

Answer 15

crzymom2u needs to look at the question again.

Answer 16

will look now but I am sure I stated it just like it was written

Answer 17

Good thinking. If the ratio is 3:5 we will get an integer answer.

Answer 18

Yeah. The ratio of the large gear to the small gear should be less than 1. I think 3:5 sounds more reasonable, which would be 0.6

Answer 19

The big gear should turn slower than the small gear, making the ratio less than 1.

Answer 20

In one machine the rpm ratio of the large gear to the small gear is 3:5 The small gear has 123 teeth

Answer 21

Ok, that changes everything.

Answer 22

thanks for getting me to look again

Answer 23

3/5=123/x means x=205

Answer 24

I think you got it!

Answer 25

thank you both so much

Answer 26

Did you work out the second part?

Answer 27

especially for also writing how you got the answer allowing me to take some notes.

Answer 28

yes I did I also got 205

Answer 29

I think the answer to the second question was 170, as noted (a long way) above.

Answer 30

yes you are correct