you have a bag with 30 fireballs and another bag with 42 jolly ranchers. for a party, you want to replace 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?
12 bags
6 bags
2 bags
3 bags
To determine 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 evenly divides both quantities.
The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30.
The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, and 42.
The common factors for both quantities are: 1, 2, 3, and 6. Therefore, the GCD is 6.
Since you want each bag to have the same number of fireballs and jolly ranchers, and the GCD is 6, you will be able to make 6 bags. Therefore, the correct answer is 6 bags.
To determine the number of bags you can make with the same number of fireballs and jolly ranchers, you need to find the greatest common divisor (GCD) of the two quantities.
The GCD of 30 and 42 is 6.
Therefore, you will be able to make 6 bags with the same number of fireballs and jolly ranchers.
To find the number of bags you can make with the same number of fireballs and jolly ranchers, you need to find the greatest common divisor (GCD) of 30 and 42. The GCD is the largest number that divides both 30 and 42 without leaving a remainder.
To find the GCD, you can use either the prime factorization method or the Euclidean algorithm. Let's use the prime factorization method:
For 30:
Prime factorization of 30 = 2 * 3 * 5
For 42:
Prime factorization of 42 = 2 * 3 * 7
To find the GCD, you need to take the common prime factors using the lowest exponent for each factor: 2 * 3.
Therefore, the GCD of 30 and 42 is 2 * 3 = 6.
Since you want each bag to have the same number of fireballs and jolly ranchers, you can make bags with 6 fireballs and 6 jolly ranchers each.
To determine the number of bags you can make, divide the total number of fireballs (30) by the number of fireballs in each bag (6):
30 fireballs รท 6 fireballs per bag = 5 bags
So, you will be able to make 5 bags.