You have a bag with 30 fireballs and another bag with 42 Jolly Ranchers. For a party, you want to repackage the candy into smaller bags, and you want each bag to have the same number of fireballs and Jolly Ranchers as every other bag. How many bags will you be able to make?(1 point) Responses 12 bags
6 bags
2 bags
3 bags
To find out how many bags you can make, you need to find the greatest common divisor (GCD) of 30 (fireballs) and 42 (Jolly Ranchers).
The prime factors of 30: 2 x 3 x 5
The prime factors of 42: 2 x 3 x 7
To find the GCD, you take the common prime factors and multiply them:
GCD = 2 x 3 = 6
So, you will be able to make 6 bags, with each bag having the same number of fireballs and Jolly Ranchers.
To determine the number of bags you can make with the same number of fireballs and Jolly Ranchers, we need to find the greatest common divisor (GCD) of 30 and 42.
Step 1: Find the prime factorization of each number.
- The prime factorization of 30 is 2 x 3 x 5.
- The prime factorization of 42 is 2 x 3 x 7.
Step 2: Determine the common factors.
- Both numbers have 2 and 3 as common factors.
Step 3: Find the GCD by multiplying the common factors.
- The GCD of 30 and 42 is 2 x 3 = 6.
Step 4: Divide the total number of candies by the GCD.
- There are 30 + 42 = 72 candies in total.
- Divide 72 by 6 (the GCD) to get the number of bags that can be made.
- 72 / 6 = 12
Therefore, you will be able to make 12 bags with the same number of fireballs and Jolly Ranchers.
To find the number of bags you can make, you need to find the greatest common divisor (GCD) of 30 and 42. The GCD represents the largest number that divides both 30 and 42 evenly.
To find the GCD, you can use the Euclidean algorithm. Divide 42 by 30:
42 ÷ 30 = 1 remainder 12
Then, divide the previous divisor (30) by the remainder (12):
30 ÷ 12 = 2 remainder 6
Continue this process until you reach a remainder of zero:
12 ÷ 6 = 2 remainder 0
The final non-zero remainder is 6, which means the GCD of 30 and 42 is 6.
Since you want each bag to have the same number of fireballs and Jolly Ranchers, the number of bags you can make will be the GCD (6).
Therefore, you will be able to make 6 bags.