Richard has 10 red cards, 20 black cards and 50 yellow cards. If Richard wants to increase the percentage of red cards to 30%, how many more red cards will he need? Please explain step by step and clearly. Why does the total amount of the cards (80) have to increase as well? Why can't the 12.5% of red cards currently in the pack be increased to 30% within the 80 cards? How do we know when to increase the total amount of cards and when to increase the amount of something within the quantities given? Please link useful sites for practise on these types of questions.

Question

Reiny · Accepted Answer

Right now:
percentage of reds = 10/80 or 12.5%, you stated that.
This does not help us, and has nothing to do with the question.

Let the number of reds to be added be x
so we have 10+x reds and the total cards is now 80+x

thus:
(10 + x)/(80+x) = 30/100 = 3/10
cross-multiply ...
100 + 10x = 240 + 3x
7x = 140
x = 20

So he must add 20 red cards

check: new number of reds = 30
new number of total cards = 80+20 = 100
percentage of reds = 30/100 = 30%

The explanation is contained in the steps of my solution.

A twist to the question would be:
How many of the non-red cards would you have to remove to that your reds would be 30% of the total? Is it possible to have exactly 30% red cards?

oobleck · Answer

You have 80 cards now.
The reds are only 1/8 = 12.5%
So clearly you need more red cards. But that also adds to the total number of cards, yeah?

To rise to 30% of just 80 cards, you will need 24 red cards. That means that 14 of the other cards will have to be replaced with red cards, but that was not provided for.

Maybe you could do some google searches on your own for problems with probability.

Jiksha Lover · Answer

Thanks a lot.