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Sagot :
To determine which ordered pairs of spoonfuls of brands A and B meet Steve's requirement for the minimum milligrams of calcium, iron, and vitamins, let's analyze the table.
First, let's lay out the nutrients per spoonful for each brand:
- Brand A: 5 mg of calcium, 4 mg of iron, 7 mg of vitamins.
- Brand B: 4 mg of calcium, 6 mg of iron, 4 mg of vitamins.
We need:
- At least 24 mg of calcium,
- At least 15 mg of iron,
- At least 16 mg of vitamins.
Next, let's evaluate each pair:
1. Pair (1,4):
- Total calcium: [tex]\(1 \times 5 + 4 \times 4 = 5 + 16 = 21\)[/tex] mg,
- Total iron: [tex]\(1 \times 4 + 4 \times 6 = 4 + 24 = 28\)[/tex] mg,
- Total vitamins: [tex]\(1 \times 7 + 4 \times 4 = 7 + 16 = 23\)[/tex] mg.
2. Pair (1,5):
- Total calcium: [tex]\(1 \times 5 + 5 \times 4 = 5 + 20 = 25\)[/tex] mg,
- Total iron: [tex]\(1 \times 4 + 5 \times 6 = 4 + 30 = 34\)[/tex] mg,
- Total vitamins: [tex]\(1 \times 7 + 5 \times 4 = 7 + 20 = 27\)[/tex] mg.
3. Pair (2,3):
- Total calcium: [tex]\(2 \times 5 + 3 \times 4 = 10 + 12 = 22\)[/tex] mg,
- Total iron: [tex]\(2 \times 4 + 3 \times 6 = 8 + 18 = 26\)[/tex] mg,
- Total vitamins: [tex]\(2 \times 7 + 3 \times 4 = 14 + 12 = 26\)[/tex] mg.
4. Pair (3,2):
- Total calcium: [tex]\(3 \times 5 + 2 \times 4 = 15 + 8 = 23\)[/tex] mg,
- Total iron: [tex]\(3 \times 4 + 2 \times 6 = 12 + 12 = 24\)[/tex] mg,
- Total vitamins: [tex]\(3 \times 7 + 2 \times 4 = 21 + 8 = 29\)[/tex] mg.
5. Pair (4,1):
- Total calcium: [tex]\(4 \times 5 + 1 \times 4 = 20 + 4 = 24\)[/tex] mg,
- Total iron: [tex]\(4 \times 4 + 1 \times 6 = 16 + 6 = 22\)[/tex] mg,
- Total vitamins: [tex]\(4 \times 7 + 1 \times 4 = 28 + 4 = 32\)[/tex] mg.
Now, verify which pairs meet all three nutrient requirements:
- [tex]\((1, 4)\)[/tex]: Calcium 21 mg (Insufficient).
- [tex]\((1, 5)\)[/tex]: Calcium 25 mg, Iron 34 mg, Vitamins 27 mg (Sufficient).
- [tex]\((2, 3)\)[/tex]: Calcium 22 mg (Insufficient).
- [tex]\((3, 2)\)[/tex]: Calcium 23 mg (Insufficient).
- [tex]\((4, 1)\)[/tex]: Calcium 24 mg, Iron 22 mg, Vitamins 32 mg (Sufficient).
Hence, the ordered pairs (1, 5) and (4, 1) meet all the requirements. The correct answers are:
(1, 5) and (4, 1)
First, let's lay out the nutrients per spoonful for each brand:
- Brand A: 5 mg of calcium, 4 mg of iron, 7 mg of vitamins.
- Brand B: 4 mg of calcium, 6 mg of iron, 4 mg of vitamins.
We need:
- At least 24 mg of calcium,
- At least 15 mg of iron,
- At least 16 mg of vitamins.
Next, let's evaluate each pair:
1. Pair (1,4):
- Total calcium: [tex]\(1 \times 5 + 4 \times 4 = 5 + 16 = 21\)[/tex] mg,
- Total iron: [tex]\(1 \times 4 + 4 \times 6 = 4 + 24 = 28\)[/tex] mg,
- Total vitamins: [tex]\(1 \times 7 + 4 \times 4 = 7 + 16 = 23\)[/tex] mg.
2. Pair (1,5):
- Total calcium: [tex]\(1 \times 5 + 5 \times 4 = 5 + 20 = 25\)[/tex] mg,
- Total iron: [tex]\(1 \times 4 + 5 \times 6 = 4 + 30 = 34\)[/tex] mg,
- Total vitamins: [tex]\(1 \times 7 + 5 \times 4 = 7 + 20 = 27\)[/tex] mg.
3. Pair (2,3):
- Total calcium: [tex]\(2 \times 5 + 3 \times 4 = 10 + 12 = 22\)[/tex] mg,
- Total iron: [tex]\(2 \times 4 + 3 \times 6 = 8 + 18 = 26\)[/tex] mg,
- Total vitamins: [tex]\(2 \times 7 + 3 \times 4 = 14 + 12 = 26\)[/tex] mg.
4. Pair (3,2):
- Total calcium: [tex]\(3 \times 5 + 2 \times 4 = 15 + 8 = 23\)[/tex] mg,
- Total iron: [tex]\(3 \times 4 + 2 \times 6 = 12 + 12 = 24\)[/tex] mg,
- Total vitamins: [tex]\(3 \times 7 + 2 \times 4 = 21 + 8 = 29\)[/tex] mg.
5. Pair (4,1):
- Total calcium: [tex]\(4 \times 5 + 1 \times 4 = 20 + 4 = 24\)[/tex] mg,
- Total iron: [tex]\(4 \times 4 + 1 \times 6 = 16 + 6 = 22\)[/tex] mg,
- Total vitamins: [tex]\(4 \times 7 + 1 \times 4 = 28 + 4 = 32\)[/tex] mg.
Now, verify which pairs meet all three nutrient requirements:
- [tex]\((1, 4)\)[/tex]: Calcium 21 mg (Insufficient).
- [tex]\((1, 5)\)[/tex]: Calcium 25 mg, Iron 34 mg, Vitamins 27 mg (Sufficient).
- [tex]\((2, 3)\)[/tex]: Calcium 22 mg (Insufficient).
- [tex]\((3, 2)\)[/tex]: Calcium 23 mg (Insufficient).
- [tex]\((4, 1)\)[/tex]: Calcium 24 mg, Iron 22 mg, Vitamins 32 mg (Sufficient).
Hence, the ordered pairs (1, 5) and (4, 1) meet all the requirements. The correct answers are:
(1, 5) and (4, 1)
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