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At a summer festival, each visitor to a smoothie booth ordered exactly one smoothie, either a small smoothie or a large smoothie. A small smoothie contains 2 servings of fruit, and a large smoothie contains 3 servings of fruit. How many visitors ordered the large smoothie?
(1) A total of 210 servings of fruit were used for the smoothies.
(2) 80 percent of the visitors to the smoothie booth ordered the large smoothie.
(1) A total of 210 servings of fruit were used for the smoothies.
(2) 80 percent of the visitors to the smoothie booth ordered the large smoothie.
13 Jan 2026, 11:02
Kudos
Bookmarks
Official Solution:
At a summer festival, each visitor to a smoothie booth ordered exactly one smoothie, either a small smoothie or a large smoothie. A small smoothie contains 2 servings of fruit, and a large smoothie contains 3 servings of fruit. How many visitors ordered the large smoothie?
(1) A total of 210 servings of fruit were used for the smoothies.
Let S be the number of small smoothies and L be the number of large smoothies. Then 2S + 3L = 210. There are multiple possible values of L. Not sufficient.
Notice that, since each visitor ordered exactly one smoothie, S is also the number of visitors who ordered a small smoothie, and L is also the number of visitors who ordered a large smoothie.
(2) 80 percent of the visitors to the smoothie booth ordered the large smoothie.
This implies that the ratio of the number of visitors who ordered a large smoothie to the number of visitors who ordered a small smoothie is 80 to 20, or 4 to 1. Thus, L/S = 4. Not sufficient.
(1)+(2) From (2), L = 4S. Substituting into 2S + 3L = 210 gives 2S + 3(4S) = 210, so S = 15. Therefore L = 60. Sufficient.
Answer: C
At a summer festival, each visitor to a smoothie booth ordered exactly one smoothie, either a small smoothie or a large smoothie. A small smoothie contains 2 servings of fruit, and a large smoothie contains 3 servings of fruit. How many visitors ordered the large smoothie?
(1) A total of 210 servings of fruit were used for the smoothies.
Let S be the number of small smoothies and L be the number of large smoothies. Then 2S + 3L = 210. There are multiple possible values of L. Not sufficient.
Notice that, since each visitor ordered exactly one smoothie, S is also the number of visitors who ordered a small smoothie, and L is also the number of visitors who ordered a large smoothie.
(2) 80 percent of the visitors to the smoothie booth ordered the large smoothie.
This implies that the ratio of the number of visitors who ordered a large smoothie to the number of visitors who ordered a small smoothie is 80 to 20, or 4 to 1. Thus, L/S = 4. Not sufficient.
(1)+(2) From (2), L = 4S. Substituting into 2S + 3L = 210 gives 2S + 3(4S) = 210, so S = 15. Therefore L = 60. Sufficient.
Answer: C
