Question

A box contained red, orange and white beads, 20% of the beads were red. Later, the number

of red beads was increased by 5% and the total number of orange beads and white beads
were increased by half. Mary found that there were 123 beads more. How many beads were in the
box at first?

Answer 1

Explanation:

Let the total number of beads in the box be x.

Then, the number of red beads in the box is 20% of x = 0.2x.

After increasing the number of red beads by 5%, the number of red beads becomes 1.05 times the original number of red beads, which is 1.05(0.2x) = 0.21x.

The total number of orange and white beads is (100% - 20%) = 80% of x, which is 0.8x.

After increasing the number of orange and white beads by half, the total number becomes 1.5 times the original number, which is 1.5(0.8x) = 1.2x.

So, we have the equation: 0.21x = 0.2x + 123 - 1.2x

Simplifying this equation, we get:

0.01x = 123

x = 12,300

Therefore, the box originally contained 12,300 beads.