How many green marbles need to be taken out to have a total of 52% green?

Question

Okay, so my question is...If there are 150 marbles total in a bag with 90 of them green and 60 are red, how many green marbles need to be taken out to have 52% of them green?

Answer 1

x=# of green marbles

x/(60+x)=52%

x/(60+x)=0.52

x=0.52(60+x)

x=31.2+0.52x

x-0.52x=31.2

0.48x=31.2

48x=3120

x=3120/48

x=65

you want only 65 green marbles so you must take out 90-65=25 green marbles

65 green and 60 red give us 125 marbles

65/125=13/25=52/100=52%

Answer 2

If you remove n green marbles the requirement is that

(90-n)/(150-n)=.52 the percentage of green marbles in the final mixture

90-n=.52(150-n)=78-.52n

12=.48n

25=n