Carlos is packing snacks for treats at a party. Every sack has exactly the same treats in it. Carlos has 96 granola bars and 64 small popcorn balls. What is the greatest number of treat sacks Carlos can make? How many of each kind of treat is in each sack?
GCF(96,64) = 32
So he can make 32 bags, each with 3 granola and 2 popcorn
Plz help me with this question
To find the greatest number of treat sacks Carlos can make, we need to determine the greatest common divisor (GCD) of 96 and 64. The GCD represents the largest possible number of sacks that can be made with equal numbers of granola bars and popcorn balls.
To find the GCD, we can use the Euclidean algorithm. We divide the larger number (96) by the smaller number (64) and find the remainder.
96 ÷ 64 = 1 remainder 32
We then divide the previous divisor (64) by the remainder (32) and again find the remainder.
64 ÷ 32 = 2 remainder 0
Since we reached a remainder of 0, the last non-zero remainder we had was 32. Therefore, the GCD of 96 and 64 is 32.
Now that we know the GCD is 32, it means Carlos can make 32 treat sacks with equal numbers of granola bars and popcorn balls.
To find out how many of each kind of treat is in each sack, we divide the total number of each treat by the number of treat sacks we determined (32).
For the granola bars:
96 granola bars ÷ 32 treat sacks = 3 granola bars per sack
For the popcorn balls:
64 popcorn balls ÷ 32 treat sacks = 2 popcorn balls per sack
Therefore, Carlos can make 32 treat sacks, and each sack will contain 3 granola bars and 2 popcorn balls.