Question

There are 25 red beads,x blue beads and y green beads in a box.When a bead is picked at random,the probability that it is blue is 1 over 4 and the probability that it is green is 1 over 3.
(a)Find the value of x and y.
(b)How many blue beads must be added so that the probability of picking a blue bead is 4 over 13?

Answer:a. X=15, y=20
b. 5

Thanks..

Answer 1

x=blue, y=green

x/(25+x+y)=1/4
Cross multiply and simplify
4x=25+x+y => 3x-y=25

y/(25+x+y)=1/3
Cross multiply and simplify
3y=25+x+y => -x+2y=25

Solving:
5x=75 => x=15
y=3*15-25=20

z+15/(60+z)=4/13
Cross multiply
13(z+15)=4(60+z)
9z=45
z=5
5 blue beads must be added.