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.
+129899 ¸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
