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
12 bags
6 bags
6 bags
2 bags
2 bags
3 bags
3 bags
To find out how many bags you can make, you need to find the greatest common divisor (GCD) of the number of fireballs and Jolly Ranchers.
The GCD of 30 and 42 is 6.
Therefore, you will be able to make 6 bags, with each bag containing 5 fireballs and 7 Jolly Ranchers.
To find out how many bags you can make with the given number of fireballs and Jolly Ranchers, you need to find the greatest common factor (GCF) of 30 and 42. The GCF is the largest number that can evenly divide both numbers.
To find the GCF, you can use a method called prime factorization.
First, find the prime factors of 30:
30 = 2 * 3 * 5
Next, find the prime factors of 42:
42 = 2 * 3 * 7
Now, identify the common prime factors between the two numbers:
Both numbers have 2 and 3 as prime factors, so they are common factors.
To find the GCF, we multiply the common prime factors:
GCF = 2 * 3 = 6
So, the GCF of 30 and 42 is 6.
To determine how many bags you can make, divide the total number of fireballs (30) and Jolly Ranchers (42) by the GCF (6):
Number of bags = (30 + 42) / 6 = 72 / 6 = 12
Therefore, you will be able to make 12 bags with the same number of fireballs and Jolly Ranchers.