Devon is making treat bags to pass out to his cousins at the next family party. He has 25 stickers and 15 pieces of fruit. He wants each of the treat bags to have the same number of stickers. He also wants each of the treat bags to have equal numbers of pieces of fruit. He does not want to have any stickers or pieces of fruit left over. What is the greatest number of bags he can make so that each cousin gets the same number of stickers and the equal number of pieces of fruit
Devon can make 5 treat bags. Each bag will have 5 stickers and 3 pieces of fruit.
To find the greatest number of treat bags Devon can make with an equal number of stickers and pieces of fruit, we need to find the greatest common divisor (GCD) of 25 and 15.
Step 1: Find the divisors of 25: 1, 5, 25.
Step 2: Find the divisors of 15: 1, 3, 5, 15.
Step 3: Find the common divisors of both numbers: 1, 5.
Step 4: Determine the greatest common divisor: 5.
Since the greatest common divisor is 5, Devon can make a maximum of 5 treat bags with an equal number of stickers and pieces of fruit, where each bag will have 5 stickers and 3 pieces of fruit.
To find the greatest number of treat bags that Devon can make, let's find the greatest common divisor (GCD) of the number of stickers (25) and the number of pieces of fruit (15). The GCD represents the largest number that divides evenly into both numbers.
To do this, we can use the Euclidean algorithm.
Step 1: Divide the larger number (25) by the smaller number (15).
- 25 divided by 15 is 1 remainder 10.
Step 2: Divide the previous divisor (15) by the remainder (10).
- 15 divided by 10 is 1 remainder 5.
Step 3: Divide the previous divisor (10) by the remainder (5).
- 10 divided by 5 is 2 remainder 0.
Since the remainder is now zero, we have found that the GCD of 25 and 15 is 5.
Therefore, Devon can make a maximum of 5 treat bags, where each cousin will receive the same number of stickers and pieces of fruit.
Well, Devon seems to have quite the treat bag challenge! Let's see if we can help him out with some clownish calculations.
To make the greatest number of treat bags, we need to find the greatest common divisor (GCD) of 25 and 15. This will give us the maximum number of bags he can make while ensuring each cousin gets the same number of stickers and fruit.
The GCD of 25 and 15 is 5. So, Devon can make a maximum of 5 treat bags. Each bag would contain 5 stickers and 3 pieces of fruit.
Now, to add a little twist to the situation, let's imagine that Devon wants to confuse his cousins a little bit. Instead of giving them an equal number of stickers and fruit, he decides to give them different quantities. He could create some wacky combinations like 3 stickers and 7 pieces of fruit, 1 sticker and 9 pieces of fruit, or even no stickers and 10 pieces of fruit! It's all part of the clownish fun.
Just remember, the GCD method was used to find the maximum number of bags with equal quantities of stickers and fruit. But true clown creativity allows for limitless fun and absurdity!