Question

Brianna wants to create snack bags for a trip she is going on. She has 15 granola bars and 10 pieces of dried fruit. If the snack bags should be identical without any food left over, what is the greatest number of snack bags Brianna can make?

Answer 1

The greatest number of identical snack bags Brianna can make is 5, with each bag containing 3 granola bars and 2 pieces of dried fruit. This is found by calculating the Greatest Common Divisor (GCD) of 15 and 10 and using it to divide the items evenly.

Step-by-step explanation:

The greatest number of snack bags Brianna can make without any food left over is defined by the highest number that can evenly divide both 15 granola bars and 10 pieces of dried fruit. This is known as the Greatest Common Divisor (GCD). To find the GCD, we list the factors of each number and then identify the largest factor that is common to both numbers.

Factors of 15 are 1, 3, 5, 15. Factors of 10 are 1, 2, 5, 10. The largest common factor is 5. Therefore, Brianna can make a total of 5 identical snack bags with 3 granola bars and 2 pieces of dried fruit in each bag.

Step-by-step:

1. List the factors of the total number of granola bars (15) and dried fruits (10).

2. Identify the common factors between the two sets of factors.

3. Find the largest number in the common factors which is the GCD.

4. Divide the total number of granola bars and dried fruits by the GCD to determine how many of each will go into each snack bag.