Question

A box contains red, blue, and yellow beads. 1/4 of the beads are red. 2/9 of the remaining beads are blue. What fraction of the beads in the box are yellow?

Answer 1

x = number of beads

1 / 4 of the beads are red.

x / 4 of the beads are red.

The remainder is:

x - x / 4 = 4 x / 4 - x / 4 = 3 x / 4

2 / 9 of the remaining beads are blue means:

( 2 / 9 ) • ( 3 x / 4 ) = 2 • 3 x / 9 • 4 =

6 x / 36 = 6 • x / 6 • 6 = x / 6

are blue beads.

x / 6 of the beads are blue.

red beads + blue beads =

3 x / 4 + x / 6 =

3 • 3 x / 3 • 4 + 2 • x / 2 • 6 =

9 x / 12 + 2 x / 12 = 11 x / 12

Yellow beads:

x - 11 x / 12 =

12 x / 12 - 11 x / 12 = x / 12

1 / 12 of the beads in the box are yellow.