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

there were 300 beads in the box at first.

Explanation:

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

Then, the number of red beads initially is 0.2x.

After the increase of 5%, the number of red beads becomes 1.05(0.2x) = 0.21x.

The total number of non-red beads (orange and white) initially is 0.8x.

After the increase of half, the total number of non-red beads becomes 1.5(0.8x) = 1.2x.

The total number of beads after all the increases is (0.21x) + (1.2x) = 1.41x.

Since there are 123 more beads, we can write:

1.41x - x = 123

0.41x = 123

x = 300

Therefore, there were 300 beads in the box at first.