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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?

tertre  Feb 16, 2018
edited by tertre  Feb 16, 2018
 #1
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+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.

Guest Feb 16, 2018
edited by Guest  Feb 16, 2018
 #2
avatar+91097 
+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

 

 

cool cool cool

CPhill  Feb 16, 2018
 #3
avatar+3270 
+1

Thank you CPhill and guest!

tertre  Feb 16, 2018

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