+0

0
176
3
+3729

A bag contains 4 blue, 5 green and 3 red marbles. How many green marbles must be added to the bag so that 75 percent of the marbles are green?

Feb 16, 2018
edited by tertre  Feb 16, 2018

#1
+1

5+4+3 =12 - total number of marbles

5/12 =41.67%

Let the number of extra green marbles =G

[G+5] / [3+4+5 + G] =0.75

Solve for G:

(G + 5)/(G + 12) = 0.75

0.75 = 3/4:

(G + 5)/(G + 12) = 3/4

Cross multiply:

4 (G + 5) = 3 (G + 12)

Expand out terms of the left hand side:

4 G + 20 = 3 (G + 12)

Expand out terms of the right hand side:

4 G + 20 = 3 G + 36

Subtract 3 G + 20 from both sides:

G = 16 - Extra green marbles will be needed to make 75% of the total.

Proof: 16 + 5 =21 - Green marbles

3 + 4 + 21 = 28 - marbles in total, so that:

21 / 28 =75% - are green marbles.

Feb 16, 2018
edited by Guest  Feb 16, 2018
#2
+94526
+1

¸We have a total of 12 marbles....let x be the number of green ones we need to add

[ Green + Added Green ] / [ Total + Added Green ]  = .75  = 3/4

[ 5 + x ] / [ 12 + x ]   =   3/4    cross-multiply

4 [ 5 + x ] =  3[ 12 + x ]    simplify

20 + 4x  =   36 + 3x      subtract  3x, 20 from both sides

x  = 16 ⇒    16 green must be added

Feb 16, 2018
#3
+3729
+1

Thank you CPhill and guest!

Feb 16, 2018