A carnival game gives variety bags as prizes. The game operator uses 100 balloons and 68 stickers to put into a certain number of bags. How many balloons and how many stickers can go in each bag if they make the greatest number of bags possible so that each bag has the same number of balloons and the same number of stickers?(1 point)

Question

Responses

17 balloons and 25 stickers
17 balloons and 25 stickers

25 balloons and 17 stickers
25 balloons and 17 stickers

4 balloons and 4 stickers
4 balloons and 4 stickers

50 balloons and 34 stickers
50 balloons and 34 stickers

Answer 1

To solve the problem, we need to find the greatest common divisor (GCD) of the number of balloons (100) and the number of stickers (68). This will determine the maximum number of bags we can create while keeping the same number of balloons and stickers in each bag.

1. Find the GCD of 100 and 68:

   • The factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100
   • The factors of 68 are: 1, 2, 4, 17, 34, 68
   • The common factors of 100 and 68 are: 1, 2, 4
   • The greatest common factor is 4.

2. Determine how many balloons and stickers go in each bag:

   • To find out how many bags can be made, we divide the total number of balloons and stickers by the GCD:
     • Balloons per bag: 100 balloons / 4 bags = 25 balloons
     • Stickers per bag: 68 stickers / 4 bags = 17 stickers

Therefore, the maximum number of bags that can be created while maintaining equal amounts is 4 bags, with each bag containing 25 balloons and 17 stickers.

The correct response is: 25 balloons and 17 stickers.