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A grocer carries two types of frozen meals that have the fat and carbohydrate content shown in the table above. John wants to purchase a combination of the two types of meals with no more than 350 grams of fat and no more than 2975 grams of carbohydrates. If John purchases 10 Szechuan chicken meals, what is the greatest number of stir‑fry meals he can purchase so that the combination will satisfy the requirements?

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Based on the table, 10 Szechuan chicken meals contain (5)(10) = 50 grams of fat and (35)(10) = 350 grams of carbohydrates.

So the greatest number of stir-fry meals that John can purchase must contain no more than 350 – 50 = 300 grams of fat and no more than 2975 – 350 = 2625 grams of carbohydrates.

It follows that the greatest number of stir-fry meals he can purchase so that the combination will satisfy the fat requirement is:

300/4 = 75,

and the greatest number of stir-fry meals he can purchase so that the combination will satisfy the carbohydrate requirement is:

2625/40 = 65625

Since John cannot purchase parts of a meal and purchasing 66 stir-fry meals would exceed the carbohydrate requirement, the greatest number of meals he can purchase so that the carbohydrate requirement will be satisfied is 65.

Therefore, the greatest number of stir-fry meals he can purchase so that the combination will satisfy both requirements is 65.

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