Answer:
45 and 38
Explanation:
Note that ratio of 2 gears are N1/N2 such that N1 is the first gear, N2 is the second gear
N1/N2 = 1.1839323 =
=
Express this as continued function, we will get as follows
1; 5, 2, 3, 2, 5, .....
Using this continued function, try find the least error while trying to find the combination of nominator and denominator with both less than 50
[1;] = 1 error -0.1839323 1/1
[1;3] = 1.33... error +0.1494010 4/3
[1;4] = 1.25 error +0.0660677 5/4
[1;5] = 1.2 error +0.0160677 6/5
[1;5,2] = 1.18182 error -0.002114118 13/11
[1;5,2,2] = 1.185185 error +0.001253 32/27
[1;5,2,3] = 1.184210 error +0.000278 45/38
[1;5,2,3,1] = 1.183673 error -0.0002588 58/49
[1;5,2,3,2] = 1.18391 error -0.000024254 103/87
at [1;5,2,3,1], the value of nominator and denominator has exceeded the limit 50,
So the nearest ratio suitable for this problem is 1.184210 with ratio 45/38 i.e. gear 1 with 45 teeth, gear 2 with 38 gear.