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A shipping clerk is loading whole pallets onto a truck. The number of pallets, n, satisfies two conditions: four more than twice the number of pallets is at most 30, and when the number of pallets is subtracted from 5 and that result is multiplied by 3, the product is less than negative 9. How many integer values of n are possible?
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Correct answer
C
Translate each condition into a linear inequality, then combine them. Condition 1: four more than twice the number of pallets is at most 30, so 2n + 4 ≤ 30. Subtract 4: 2n ≤ 26. Divide by 2: n ≤ 13. Condition 2: subtract n from 5, multiply by 3, and the product is less than negative 9, so 3(5 − n) < −9. Expand: 15 − 3n < −9. Subtract 15: −3n < −24. Now divide both sides by −3, and because you are dividing by a negative number you must reverse the inequality sign: n > 8.
Combine the two results: 8 < n ≤ 13. Since n must be a whole number of pallets, the possible values are 9, 10, 11, 12, and 13, which is 5 values. The credited answer is (C) 5.
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