Question

MEDAL!!!

Balls are to be removed from an urn that contains 20 black balls and 20 white balls. What is the least number of balls that must be removed so that the ratio of black to white balls is 9 to 2?

7
11
15
18
OR 22
explains pleaseee <3

Answer 1

@blurbendy

Answer 2

@Zarkon

Answer 3

So in order to have a 9 to 2 ratio, you need to have some sort of fraction of black balls to white balls that is equivalent to 9/2. So ratios that would be equivalent to 9/2 would be fractions like 18/2, 27/6, 36/8, etc. Each of those fractions I obtained by multiplying the top and bottom of the fraction 9/2 by the same number. So I have 40 balls maximum, so the combination of the numerator + the denominator must not be greater than 40. Now going to my fractions that are all equivalent to a 9/2 ratio, the greatest fraction that does not add up to above 40 would be 27/6. So if I can remove balls as to where I have 27 black balls and 6 white balls, I will have a 9 to 2 ratio. This means I can achieve this by removing 7 balls, which be the minimum I can remove to get some ratio equal to 9 to 2.

Answer 4

OMG THANK YOU! what about if its 100 red marbles 80 blue marbles and ratio of red to blue of 4 to 3?

Answer 5

@Psymon

Answer 6

So, in this case we have a maximum of 180 marbles and we need some sort of fractional equivalent to 4/3 where the addition of numerator and denominator is under 180. So I can multiply the top and bottom of the fraction by various numbers until my fraction is as high as it can go without going over 180. So some examples of equivalent ratios would be 80/60, 100/75, etc. A 100/75 ratio is the highest ratio I can have that is still equivalent to 4/3 without going over 180. So if I can get away with having 100 red marbles and 75 blue marbles, all I need to do is to remove 5 in order to have a ratio equivalent to 4 to 3.