An anti-allergy medication contains 75% aspirin and 25% antihistamine by weight. If aspirin costs 15 cents per gram and antihistamine costs 50 cents per gram, what is the total cost to manufacture one hundred 1-gram tablets?

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Multiple Choice

An anti-allergy medication contains 75% aspirin and 25% antihistamine by weight. If aspirin costs 15 cents per gram and antihistamine costs 50 cents per gram, what is the total cost to manufacture one hundred 1-gram tablets?

Explanation:
When you mix by weight, the total cost is the sum of each component’s cost, using its weight in the mixture. Here, 100 grams total: 75 g of aspirin and 25 g of antihistamine. The aspirin costs 15 cents per gram, so its cost is 75 × 0.15 = $11.25. The antihistamine costs 50 cents per gram, so its cost is 25 × 0.50 = $12.50. Add them: $11.25 + $12.50 = $23.75. Another quick check is cost per tablet: 0.75 × 0.15 + 0.25 × 0.50 = 0.2375 dollars per tablet, and 0.2375 × 100 = $23.75. So the total manufacturing cost for one hundred 1-gram tablets is $23.75.

When you mix by weight, the total cost is the sum of each component’s cost, using its weight in the mixture. Here, 100 grams total: 75 g of aspirin and 25 g of antihistamine. The aspirin costs 15 cents per gram, so its cost is 75 × 0.15 = $11.25. The antihistamine costs 50 cents per gram, so its cost is 25 × 0.50 = $12.50. Add them: $11.25 + $12.50 = $23.75. Another quick check is cost per tablet: 0.75 × 0.15 + 0.25 × 0.50 = 0.2375 dollars per tablet, and 0.2375 × 100 = $23.75. So the total manufacturing cost for one hundred 1-gram tablets is $23.75.

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