Jason is trying to make picnic lunches.He has 12 sandwiches, 18 apples and 30 pieces of candy.How many lunches can he mmake if he wants each lunch to have the same number of each kind of food and use all of the food?
The only common factor is 6.
The question seems flawed, though, because 3 apples a piece seems a bit much.
To determine the number of lunches Jason can make with equal amounts of each kind of food and using all the food, we need to find the greatest common divisor (GCD) of the three numbers: 12, 18, and 30.
Step 1: Find the prime factorization of each number.
- Prime factorization of 12: 2 * 2 * 3
- Prime factorization of 18: 2 * 3 * 3
- Prime factorization of 30: 2 * 3 * 5
Step 2: Determine common factors.
- Common factors: 2 * 3 = 6
Step 3: Find the GCD by multiplying the common factors.
- GCD = 2 * 3 = 6
Therefore, Jason can make 6 picnic lunches with equal amounts of each kind of food.
To find out how many lunches Jason can make, we need to determine the common number of sandwiches, apples, and candies per lunch.
Step 1: Identify the limiting factor
First, we need to determine which food item is the limiting factor. The limiting factor is the food item that will determine the maximum number of lunches Jason can make. In this case, since we want each lunch to have the same number of each kind of food, we need to find the smallest number of sandwiches, apples, and candies.
Step 2: Calculate the common number of each kind of food per lunch
To find the common number of sandwiches, apples, and candies per lunch, we need to divide the quantity of each food item by the smallest number we found in Step 1.
The smallest number of sandwiches = 12
The smallest number of apples = 18
The smallest number of candies = 30
Now, we divide each quantity by the smallest number:
Number of sandwiches per lunch = 12 / 12 = 1
Number of apples per lunch = 18 / 18 = 1
Number of candies per lunch = 30 / 30 = 1
Step 3: Determine the number of lunches Jason can make
Since the common number of each kind of food per lunch is 1, Jason can make a total of 1 lunch using all the food items.
Therefore, Jason can make 1 lunch if he wants each lunch to have the same number of each kind of food and use all of the food.