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?

Question

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?

Answer 1

t = r + y + 48

 

r = t/4

 

y = (3/5)(t - r)

= (3/5)(t - t/4) 

= (3/5)(3t/4)

= 9t/20

 

t = t/4 + 9t/20 + 48

Multiply through by 20 to clear fractions

20t = 5t + 9t + 960

6t = 960

t = 160 beads in total

 

check:

r = t/4 = 40 red beads

y = 9t/20 = 72 yellow beads

b = 48 blue beads

 

40 + 72 + 48 = 160 beads