Final answer:
The greatest number of identical coupon booklets that can be created from 32 dry-cleaning coupons, 80 restaurant coupons, and 48 movie theater coupons is 16, which is found by determining the greatest common divisor of the three numbers. However, the correct answer is not listed in the provided options.
Step-by-step explanation:
To find the greatest number of identical coupon booklets you can create with 32 dry-cleaning coupons, 80 coupons for local restaurants, and 48 movie theater coupons, you need to determine the greatest common divisor (GCD) of those three numbers. The GCD is the largest number that divides all three without leaving a remainder. This can be done by factorizing each number or by using the Euclidean algorithm.
Upon finding the factors of each, we find that:
- 32 is divisible by 1, 2, 4, 8, 16, and 32
- 80 is divisible by 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80
- 48 is divisible by 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48
The largest number that appears in all three sets is 16. Therefore, the greatest number of identical coupon booklets you can create is 16.
The correct answer is not listed among the options provided. However, if you had to pick from the provided choices, it is better to identify that 16 is not an option and not select an answer, as none of them is correct.