Q:

Maria Camila, Sebastián and Juliana are friends. All three have birthdays today and they want to celebrate. Maria Camila has brought 24 candies to class to distribute, Sebastián 48 candy clouds and Juliana, since she is the stingiest, only brings 18 bittersweet candies. If you want to distribute the candy among your friends so that everyone has the same amount of each candy and it is as large as possible, how many of your friends can you give candy to? How many sweets are left for Maria Camila, Sebastián and Juliana?

Accepted Solution

A:
To find out how many friends can receive candy and how many candies are left, we need to find the greatest common divisor (GCD) of the three numbers - 24, 48, and 18.

Let's calculate the GCD:
$$\text{GCD}(24, 48, 18)$$

First, let's find the GCD of 24 and 48:
$$\text{GCD}(24, 48)$$

To find the GCD, we can use the Euclidean algorithm:
$$\text{GCD}(24, 48) = \text{GCD}(24, 48-24)$$
$$\text{GCD}(24, 48) = \text{GCD}(24, 24)$$

Since the two numbers are the same, the GCD is 24.

Now, let's find the GCD of 24 and 18:
$$\text{GCD}(24, 18)$$

Using the Euclidean algorithm:
$$\text{GCD}(24, 18) = \text{GCD}(18, 24-18)$$
$$\text{GCD}(24, 18) = \text{GCD}(18, 6)$$

Now, let's find the GCD of 18 and 6:
$$\text{GCD}(18, 6)$$

Using the Euclidean algorithm:
$$\text{GCD}(18, 6) = \text{GCD}(6, 18-3(6))$$
$$\text{GCD}(18, 6) = \text{GCD}(6, 0)$$

Since we have reached 0, the GCD is 6.

Now, let's find the GCD of 24, 48, and 18:
$$\text{GCD}(24, 48, 18) = \text{GCD}(\text{GCD}(24, 48), 18)$$
$$\text{GCD}(24, 48, 18) = \text{GCD}(24, 18)$$
$$\text{GCD}(24, 48, 18) = 6$$

The greatest common divisor of 24, 48, and 18 is 6.

Therefore, Maria Camila, Sebastián, and Juliana can all receive candy, and each of them will receive 6 candies.

To find the candies left for Maria Camila, Sebastián, and Juliana, we subtract the total number of candies distributed from the total number of candies they brought.

Maria Camila brought 24 candies and will receive 6, so she has 24 - 6 = 18 candies left.

Sebastián brought 48 candies and will receive 6, so he has 48 - 6 = 42 candy clouds left.

Juliana brought 18 candies and will receive 6, so she has 18 - 6 = 12 bittersweet candies left.

Answer:
- Each friend can receive 6 candies.
- Maria Camila has 18 candies left.
- Sebastián has 42 candy clouds left.
- Juliana has 12 bittersweet candies left.