# I Simple Math Prob

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1. Mar 30, 2016

### 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.

2. Mar 30, 2016

### 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 ?

3. Mar 30, 2016

### 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

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4. Mar 31, 2016

### zak100

Hi,

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

X = 35

Actually 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 =35

x = 22

Total red balls = 22 + 10 = 32

This is a wrong answer. Is it possible to do it in that way.

Zulfi.

5. Mar 31, 2016

### 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.

6. Mar 31, 2016

### zak100

Hi,
How can we determine the remaining 35%?

Zulfi.

7. Mar 31, 2016

### HallsofIvy

Staff Emeritus
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.

Last edited by a moderator: Mar 31, 2016
8. Mar 31, 2016

### Andrew Mason

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

Last edited: Apr 1, 2016
9. Oct 18, 2016

### 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.