In a box, 1/4 of the beads are red, 3/5 of the remainder are yellow, and the rest are blue. If there are 48 blue beads, how many beads are there altogether?

160 total beads

Step-by-step explanation:

so if 1/4 of the beads are red, then 3/4 of them are not ... so 3/4 is the remainder of beads ... and 3/5 of the remainder are yellow ... so 3/5 of 3/4 =

3/5 * 3/4 = 9/20 ... so 9/20 are yellow ... and the rest (48) are blue.

1/4 + 9/20 = 5/20 + 9/20 = 14/20 reduces to 7/10 ... so 7/10 of the beads are red and yellow

so if 7/10 of the beads are red and yellow, then 3/10 are blue

3/10 of what number is 48

3/10x = 48

x = 48 * 10/3

x = 480/3

x = 160

let me check it ...

1/4 are red ... 160 total beads ... so red beads = (1/4 * 160) = 160/4 = 40

3/5 of the remainder is yellow ... so 3/5 of (160 - 40) = 3/5 (120) = 72 yellow

and then u have 48 blue ...

40 + 72 + 48 = 160

so there are 160 total beads ... 40 red, 72 yellow, and 48 blue <===