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.
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?
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.
Thanks a lot.
To solve this problem, we need to first determine the desired number of red cards, given that the total number of cards is 80.
Step 1: Calculate the current number of red cards.
Richard currently has 10 red cards out of a total of 80 cards. Thus, the current percentage of red cards is (10/80) * 100 = 12.5%.
Step 2: Calculate the number of red cards needed to achieve a 30% ratio.
We assume the total number of cards remains at 80, so we want the number of red cards to be (30/100) * 80 = 24.
Step 3: Calculate the number of additional red cards required.
To find out how many more red cards Richard needs, subtract the current number of red cards from the desired number: 24 - 10 = 14.
So, Richard would need 14 more red cards to increase the percentage to 30%.
Now let's address your other questions:
1. Why does the total amount of cards (80) have to increase as well?
In this problem, we assume the total number of cards remains constant at 80. If we increase the percentage of red cards without increasing the total number, it would result in changing the number of cards of other colors, thereby not satisfying the problem's constraints.
2. Why can't the 12.5% of red cards currently in the pack be increased to 30% within the 80 cards?
To increase the percentage of red cards from 12.5% to 30%, we need to increase both the number of red cards and the total number of cards. If we only had 80 cards and wanted to increase the percentage of red cards, it would mean either decreasing the number of cards of other colors or increasing the number of red cards disproportionately, violating the given quantities.
3. How do we know when to increase the total amount of cards and when to increase the amount of something within the quantities given?
In this problem, the constraints are clear: Richard has a fixed number of 80 cards and wants to increase the percentage of red cards within that total. Whenever you encounter a problem with fixed quantities and want to change a percentage, you need to keep the total amount constant and adjust the specific quantity (cards in this case) to achieve the desired percentage.
To practice similar questions, you can visit the following websites:
1. Khan Academy: https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-ratios-prop-topic#cc-7th-percent/ratios-proportions
2. MathisFun: https://www.mathsisfun.com/percentage.html
3. IXL: https://www.ixl.com/math/grade-7/percent-of-change