Question

In a collection of white, red, and purple marbles, there are 35% more white marbles than red marbles,
and there are 60% more purple marbles than white marbles. If B is the number of white marbles, what
is the total number of marbles?​

Answer 1

Given:

There are white, red and purple marbles.

There are 35% more white marbles than red marbles.

There are 60% more purple marbles than white marbles.

Number of white marbles = B

To Find:

Total number of marbles

Solution

Find the number of red marbles in term of B:

Let the number of red marbles = x

Number of white marbles = x + 0.35x

Number of white marbles = 1.35x

white marbles = 1.35x

white marbles = B

1.35x = B

x = B ÷ 1.35

x = 20/27 B

Find the number of purple marbles:

Purple marbles = 60% more than white marbles

Purple marbles = B + 0.6B

Purple marbles = 1.6B

Purple marbles = 8/5 B

Find the total marbles:

White marbles = B

Red marbles  = 20/27 B

Purple marbles = 8/5 B

Total marbles = B + 20/27 B + 8/5 B

Total marbles = 452/135 B

Answer: 452/135 B