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What is the minimum number of tablets
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14 Jun 2021, 10:00
14 Jun 2021, 10:00
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Question Stats:
40% (03:15) correct
60% (02:29) wrong based on 15 sessions
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The vitamin content for three elements—iron, calcium, and zinc—contained in three different vitamin tablets. All units are in milligrams.
What is the minimum number of tablets a person can take, using any combination of the three types of tablets, in order to obtain at least 140 mg of iron and at least 160 mg of calcium?
What is the minimum number of tablets a person can take, using any combination of the three types of tablets, in order to obtain at least 140 mg of iron and at least 160 mg of calcium?
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Re: What is the minimum number of tablets
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15 Jun 2021, 03:43
15 Jun 2021, 03:43
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Expert Reply
OE
We are trying to arrive at 140 mg of iron and 160 mg of calcium efficiently, so we might as well not consume any of Tablet Y, which is highest in zinc, the one element we have no interest in. Notice that 3 of Tablet X and 2 of Tablet Y would contain 3 × 40 + 2 × 20 = 120 + 40 = 160 mg of calcium exactly. This same combination contains 3 × 17 + 2 × 45 = 51 + 90 = 141 mg of iron, which is greater than 140, as required. This combination of 3 + 2 = 5 tablets achieves the desired quantities with very little wastage. No combination of four tablets will have sufficient amounts of both iron and calcium, so 5 is the minimum
We are trying to arrive at 140 mg of iron and 160 mg of calcium efficiently, so we might as well not consume any of Tablet Y, which is highest in zinc, the one element we have no interest in. Notice that 3 of Tablet X and 2 of Tablet Y would contain 3 × 40 + 2 × 20 = 120 + 40 = 160 mg of calcium exactly. This same combination contains 3 × 17 + 2 × 45 = 51 + 90 = 141 mg of iron, which is greater than 140, as required. This combination of 3 + 2 = 5 tablets achieves the desired quantities with very little wastage. No combination of four tablets will have sufficient amounts of both iron and calcium, so 5 is the minimum
Re: What is the minimum number of tablets
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06 Mar 2025, 22:11
06 Mar 2025, 22:11
Carcass wrote:
OE
We are trying to arrive at 140 mg of iron and 160 mg of calcium efficiently, so we might as well not consume any of Tablet Y, which is highest in zinc, the one element we have no interest in. Notice that 3 of Tablet X and 2 of Tablet Y would contain 3 × 40 + 2 × 20 = 120 + 40 = 160 mg of calcium exactly. This same combination contains 3 × 17 + 2 × 45 = 51 + 90 = 141 mg of iron, which is greater than 140, as required. This combination of 3 + 2 = 5 tablets achieves the desired quantities with very little wastage. No combination of four tablets will have sufficient amounts of both iron and calcium, so 5 is the minimum
We are trying to arrive at 140 mg of iron and 160 mg of calcium efficiently, so we might as well not consume any of Tablet Y, which is highest in zinc, the one element we have no interest in. Notice that 3 of Tablet X and 2 of Tablet Y would contain 3 × 40 + 2 × 20 = 120 + 40 = 160 mg of calcium exactly. This same combination contains 3 × 17 + 2 × 45 = 51 + 90 = 141 mg of iron, which is greater than 140, as required. This combination of 3 + 2 = 5 tablets achieves the desired quantities with very little wastage. No combination of four tablets will have sufficient amounts of both iron and calcium, so 5 is the minimum
