Question

all unicorns on rainbow island are either green or yellow. every time the clock strikes midnight the unicorns change their color. Yesterday there were 6 green for every 5 yellow ones. Today there are 3 green one and 4 yellow ones. What is the smallest possible number of unicorns living on rainbow island

Answer 1

77 unicorns, because yesterday the ratio was 6:5 and today it is 3:4. If you add the numbers for both ratios together, you get 11 and 7. Finding the LCM of these two gives 77 (because 7 and 11 are both prime).

You find the LCM of the sums because when you find values based on ratios, you divide value by the sum of the ratio.

e.g. I have 100 fruits. The ratio of apples to oranges is 2:3. How many apples are there?

To solve this you'd add 2 and 3 (5), divide 100 by 5 (20), multiply that by 2 (40) because that's the ratio of apples to oranges.

In this case, you do the reverse. So If I have 77 unicorns, then yesterday there were (77/11 = 7, 7*6= 42, 7*5= 35) 42 green unicorns and 35 yellow. The sum of 42 and 35 is 77. If you do this process with the other ratio you'll get similar results as well.