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You are making snack bags to sell at the fair. You want each bag to contain the same combination of carrot and celery sticks. You have 75 carrot sticks and 40 celery sticks and want to use them all. What is the greatest number of snack bags you can make?
3 snack bags
5 snack bags
9 snack bags
15 snack bags
To find the greatest number of snack bags you can make, we need to find the greatest common divisor (GCD) of the number of carrot sticks (75) and celery sticks (40).
1. Find the GCD of 75 and 40:
– The factors of 75 are: 1, 3, 5, 15, 25, 75.
– The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40.
– The common factors are: 1, 5.
– Therefore, the GCD is 5.
2. Divide the number of sticks by the GCD:
– For carrot sticks: 75 ÷ 5 = 15
– For celery sticks: 40 ÷ 5 = 8
Now, you can divide the sticks into 5 bags (the GCD), and you’ll see that you can only fill each bag with the same combination of sticks.
To sum up, the greatest number of snack bags you can make is 5 snack bags.