Question

Lilly has a bag of 140 colored marbles. The bag has an equal number of green and blue marbles and an equal number of red and yellow marbles. If Lily arranged all of the green marbles in groups of eight and all of the blue marbles in groups of seven how many red marbles are in the bag?

Answer 1

If there are equal amounts of blue and green marbles, then there are 56 of each; so 112 altogether. That leaves 28 red and yellow marbles; therefore 14 red marbles.

Answer 2

The number of red marbles in bag are: 14

Explanation:

The bag has an equal number of green and blue marbles.

Lily arranged all of the green marbles in groups of eight and all of the blue marbles in groups of seven.

This means that the number of green and blue marbles must be a common multiple of both 8 and 7.

The common multiples of 8 and 7 are:

56 , 112,...

Now, we know that if number of green marbles are: 112

Then the number of blue marbles = 112

which exceeds the total number of marbles i.e. 140

Hence, the number of green marbles in the bag could be: 56

and number of blue marbles= 56.

Let the number of red marbles and yellow marbles each in bag = x

This means that:

56+56+x+x=140

112+2x=140

2x=140-112

2x=28

x=28/2

x=14

The number of red marbles in bag= 14