A pack of candies was shared among Angel, Helen and Rachel. Angel had 3/8 of the candies while Helen and Rachel shared the rest of the candies in the ratio 3:7. If Angel received 24 more candies than Helen, how many candies did Rachel receive?
To find out how many candies Rachel received, we first need to determine the total number of candies.
Given that Angel had 3/8 of the candies, this means the remaining fraction of candies went to Helen and Rachel. Subsequently, the fraction of candies Helen received can be represented as 1 - 3/8, which simplifies to 5/8.
Next, we are told that Angel received 24 more candies than Helen. We can set up an equation to represent this information: 3/8 of the total candies = 5/8 of the total candies - 24.
Let's solve the equation to find the total number of candies:
3/8 * Total = 5/8 * Total - 24
Multiplying through by 8 to get rid of the denominators:
3 * Total = 5 * Total - 192
Simplifying the equation:
5 * Total - 3 * Total = 192
2 * Total = 192
Dividing both sides by 2:
Total = 96
Therefore, the total number of candies is 96.
Now, let's determine how many candies Rachel received:
Since Helen and Rachel shared the remaining 5/8 of the candies in a ratio of 3:7, we can calculate Rachel's share as follows:
Rachel's share = (7 / (3 + 7)) * Total
= 7/10 * 96
= 67.2
Since we cannot have a decimal fraction of a candy, we round down to the nearest whole number.
Therefore, Rachel received 67 candies.