Harry is making gift bags for a hilarity using two types of candies. He has a total of 84 chocolate candies and 56 peppermint candies. Each gift bag he makes will be the same.
To make the gift bags, Harry needs to distribute the candy equally between them. Let's assume each gift bag will contain x chocolate candies and y peppermint candies.
Since Harry has 84 chocolate candies, the total number of chocolate candies used in all the gift bags will be 84x.
Similarly, since Harry has 56 peppermint candies, the total number of peppermint candies used in all the gift bags will be 56y.
For all the gift bags to be the same, the total number of chocolate candies and peppermint candies used in all the gift bags should be the same.
Therefore, 84x = 56y.
To find the possible values for x and y, we need to find their common factors.
The prime factorization of 84 is 2^2 * 3 * 7.
The prime factorization of 56 is 2^3 * 7.
The common factors are 2^2 * 7 = 28.
Let's divide the equation 84x = 56y by 28 to simplify it:
(84/28)x = (56/28)y.
3x = 2y.
This means for every 3 chocolate candies, Harry needs 2 peppermint candies to maintain an equal distribution in the gift bags.
Therefore, the possible values for x and y can be:
- x = 2, y = 3 (2 chocolate candies and 3 peppermint candies per gift bag).
- x = 4, y = 6 (4 chocolate candies and 6 peppermint candies per gift bag).
- x = 6, y = 9 (6 chocolate candies and 9 peppermint candies per gift bag).
- and so on.
Please note that the number of gift bags and the distribution of candies can vary based on the total number of gift bags Harry wants to make and any additional constraints.