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I Simple Math Prob

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  1. Mar 30, 2016 #1
    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. jcsd
  3. Mar 30, 2016 #2

    symbolipoint

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    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 ?
     
  4. Mar 30, 2016 #3

    Andrew Mason

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    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






    .
     
  5. Mar 31, 2016 #4
    Hi,

    Thanks for your reply:

    (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.
     
  6. Mar 31, 2016 #5

    symbolipoint

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    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.
     
  7. Mar 31, 2016 #6
    Hi,
    Thanks for your reply.
    How can we determine the remaining 35%?

    Zulfi.
     
  8. Mar 31, 2016 #7

    HallsofIvy

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    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
  9. Mar 31, 2016 #8

    Andrew Mason

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    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
  10. Oct 18, 2016 #9
    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.
     
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