Question

Luke has a bag of 70 colored marbles. The bag has an equal number of green and blue marbles and an equal number of red and yellow marbles. If Luke arranged all of the green marbles in groups of 8 and all of the blue marbles in groups of 6, how many yellow marbles are in the bag?

Answer 1

it could be over 9000 but its actually 11

Answer 2

There are 11 yellow marbles in the bag.

Explanation:

We are given the following information:

Total number of marbles in bag = 70

Number of green marble = Number of blue marbles

Number of red marbles = Number of yellow marbles

Green marbles are arranged in groups of 8 and blue marbles are arranged in groups of 6.

Number of green/blue marble = L.C.M of 8 and 6 .

`8 = 2* 2* 2\\6 = 2* 3\\L.C.M = 3* 2* 2* 2 = 24`

Thus, there are 24 green marbles and 24 blue marbles.

Thus, there are 70 - 48 = 22 red and yellow marbles.

Since, number of red and yellow marbles are equal, there are 11 red and 11 yellow marbles in the bag.