Question

Jane has 18 juice boxes, 24 bags of peanuts and 36 apples. She wants to make snack bags with same number of each thing in each bag. What is the greatest number of snack bags Jane can make?

Answer 1

Jane can make the greatest number of snack bags by finding the Greatest Common Divisor (GCD) of the quantities of items she has. The GCD of 18, 24, and 36 is 6, hence she can create 6 snack bags with an equal number of each item.

Step-by-step explanation:

Finding the Greatest Number of Snack Bags

Jane has 18 juice boxes, 24 bags of peanuts, and 36 apples, and she wants to create snack bags with an equal number of each item in each bag. To determine the greatest number of snack bags she can make, we need to find the Greatest Common Divisor (GCD) of the three numbers since the GCD will give us the largest number by which each of the items can be evenly divided

1. Find the GCD of 18, 24, and 36.
   
   • GCD of 18 and 24 is 6.
   • Now, find the GCD of 6 and 36, which is also 6.
2. Use the GCD to divide each quantity of items by 6.
   
   • 18 juice boxes ÷ 6 = 3 juice boxes per bag.
   • 24 bags of peanuts ÷ 6 = 4 bags of peanuts per bag.
   • 36 apples ÷ 6 = 6 apples per bag.
3. Therefore, Jane can make 6 snack bags with an equal number of each item.

Answer 2

Answer: 6 snack bags.

Step-by-step explanation:

For this exercise it is important to remember the Greatest Common Divisor (GCD). This is defined as the largest positive intener by which you can divided evenly "n" numbers.

In this case, you know that Jane has 18 juice boxes, 24 bags of peanuts and 36 apples. Therefore, the steps are the following:

1. You need to descompose 18, 24 and 36 into their prime factors, as below:

`18=2*3*3=2*3^2\\\\24=2*2*2*3=2^3*3\\\\36=2*2*3*3=2^2*3^2`

2. Now you must choose the common ones with the smallest exponent and multiply them.

Then, you get:

`GCD=3*2\\\\GCD=6`

Therefore, the greatest number of snack bags that Jane can make is: 6 snack bags.