Question

QUESTION:

Marine biologist counted the number of tentacles and noted the color of jellyfish in a particular area of the ocean. The ratio of pink to blue jellyfish was 5:7. Of the blue jellyfish the ratio of those with fewer than 10 tentacles to those with more than 10 tentacles was 2:3, and of the pink jellyfish the ratio of those with fewer than 10 tentacles to those with more than 10 tentacles was 5:4. (I) What percentage of the jellyfish with fewer than 10 tentacles were pink? (II) What proportion of these jellyfish are blue with more than 10 tentacles?

Please the solution to the above question has been given, not sure how they arrived that those answers, will greatly appreciate an explanation. Thank you.

Answer 1

Condition 1: The ratio of pink to blue jelly fish is 5:7

Let number of pink jelly fishes be 5x and blue jelly fishes be 7x

Condition 2: Out of blue jelly fishes (7x) , ratio of fewer than 10 tentacles vs more than 10 tentacles is 2:3

Let 2y be the no. of jelly fishes with fewer than 10 tentacles and 3y be the no. of jelly fishes with more than 10 tentacles. Thus 2y + 3y = 7x

5y=7x Thus

Condition 3:Out of pink jelly fishes (5x) , ratio of fewer than 10 tentacles vs more than 10 tentacles is 5:4

Let 5m be the no. of jelly fishes with fewer than 10 tentacles and 4m be the no. of jelly fishes with more than 10 tentacles. Thus 5m + 4m = 5x

9m = 5x Thus

i) Percentage of jelly fishes with fewer than 10 tentacles.

2y + 5m -->Total no. of fishes with less than 10 tentacles

5m --> Pink fishes with less than 10 tentacles.

Substituting and    we get

  

=49.80 %

ii)Proportion of jelly fishes are blue with more than 10 tentacles

3y + 4m -->Total no. of fishes with more than 10 tentacles

3y --> Blue fishes with less than 10 tentacles.

Substituting and    we get

  

=0.6540 or 65.4%