Craig is creating gift baskets for the food pantry to give away. He has 91 canned food items and 52 boxed food items, giving him a total of 143 items. The sum is shown below.
He wants to make sure that every gift basket has an equal amount of canned food items and an equal number of boxed food items, as well as use all of the food items.
Part A: Determine how many gift baskets he will be able to make.
Part B: Then, rewrite the sum to show how these food items will be distributed among the gift baskets.
Part C: Explain why Craig could not make any more gift baskets in this way with the available food items.
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To determine how many gift baskets Craig will be able to make, we need to find the common number of canned food items and boxed food items that can be evenly distributed among the baskets.
Part A: Let's start by finding the greatest common divisor (GCD) of 91 and 52. The GCD represents the largest number that evenly divides both numbers.
Using the Euclidean algorithm, we can find the GCD as follows:
91 ÷ 52 = 1 remainder 39
52 ÷ 39 = 1 remainder 13
39 ÷ 13 = 3 remainder 0
Since the remainder is 0, we know that 13 is the GCD of 91 and 52.
Now, we can determine how many gift baskets Craig can make by dividing the total number of items (143) by the GCD (13):
143 ÷ 13 = 11
Craig will be able to make 11 gift baskets.
Part B: To distribute the food items among the gift baskets evenly, we can divide the total number of each food item by the GCD:
Number of canned food items in each basket = 91 ÷ 13 = 7
Number of boxed food items in each basket = 52 ÷ 13 = 4
So, each gift basket will contain 7 canned food items and 4 boxed food items.
Part C: Craig cannot make any more gift baskets in this way with the available food items because the GCD represents the largest number that divides both the number of canned food items and boxed food items evenly. If there were any more baskets, the number of food items would not be divisible evenly, resulting in either leftover items or insufficient items to fill the baskets equally.