Solve Math Problem: Add Red Marbles for 60% Red

[zak100]

Hi,
I got the following problem from a GRE book. They have provided a method but i am trying to solve it using a different method. My answer is wrong.

Q.A jar contains 10 red marbles & 30 green ones. How many red marbles must be added to the jar so that 60% of the marbles will be red?Sol. Current percentage of red marbles is:

10/40 * 100 = 25%

This means we have to add 35% more red marbles:

x/(x+40) * 100 = 35

100x = 35x + 1400

65x = 1400

X= 22 (Answer is not correct).Some body please guide me what is my mistake.Zulfi.

 

[symbolipoint]

Ten red marbles, and 30 green marbles to start. This as a percent red marbles is 10/(10+30)=10/40=25/100=25%.

Question is, how many red marbles to add, r, so that the concentration of red marbles becomes 60%.
Adding the r number of red marbles will increase both the number of red marbles, AND the total number of marbles.
Now, would you use that to form a good equation, and solve it for r ?

 

[Andrew Mason]

Welcome to PF zak100!

Let x=no of red ones to be added

(X+10)/total = 60/100

Complete the expression for total in the denominator. And solve for x

AM
.

 

[zak100]

Hi,

Thanks for your reply:

(X+10)/(X+40) = 6/10

X = 35Actually this solution is provided in the book. Right now the quantity of red balls is 10 which is 25%. I want to find out the remaining 35% of the red balls & then add that quantity with 10 (which is 25%) to find the whole 60% of red balls. How I can do it in that way.x/(x+40) * 100 =35x = 22

Total red balls = 22 + 10 = 32This is a wrong answer. Is it possible to do it in that way.Zulfi.

 

[symbolipoint]

You just stated the correct equation. Solving it (the correct one, not the incorrect one) will give your "X" for how many red balls to add.

 

[zak100]

Hi,
Thanks for your reply.
How can we determine the remaining 35%?

Zulfi.

 

[HallsofIvy]

Hi,
I got the following problem from a GRE book. They have provided a method but i am trying to solve it using a different method. My answer is wrong.

Q.A jar contains 10 red marbles & 30 green ones. How many red marbles must be added to the jar so that 60% of the marbles will be red?Sol. Current percentage of red marbles is:

10/40 * 100 = 25%

This means we have to add 35% more red marbles:

This is your mistake. Percentages are always percents of some base. You cannot arithmetically combine percents of different bases.
Your "25%" is 25% of 10+ 30= 40 marbles. The "60%" that you get by adding marble is 60% of the larger number of marbles you now have after adding red marbles. Instead, let r be the number of red marbles you added. So you have 10+ r read marbles and 40+ r total marbles.

(Editted by Mentor)

From there you should be able to complete the problem.

 

[Andrew Mason]

Hi,
Thanks for your reply.
How can we determine the remaining 35%?

Zulfi.

You can't just determine the remaining 35% because the proportions change as the total number of marbles changes. (x+10)/(x+40) always gives the proportion of red marbles. 30/(x+40) always gives you the proportion of green marbles. If the proportion of red is 60% the proportion of green is 40%. So the other approach would be to set the green proportion to 40%.

AM

 

[Deepak suwalka]

We can also solve it using proportion,
Since after adding some red marbles green marbles will be $40\%$

So, the total marbles will be-
Make the proportion,

$\dfrac{30}{x}=\dfrac{40}{100}$

$40x=3000$

$x=\dfrac{3000}{40}$

$x=75$

Hence, 30 green marbles out of 75 total marbles will be $40\%$ and 45 red marbles out of 75 total marbles will be $60\%$

Since you have 10 red marbles so you need 35 more red marbles.