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Select all the correct answers.

Steve's doctor has advised him to take protein supplements. He bought two brands, Brand A and Brand B. The table gives the amount of calcium, iron, and vitamins (in milligrams per spoonful) in each of the two brands.

\begin{tabular}{|c|r|r|r|}
\hline Brand & Calcium & Iron & Vitamins \\
\hline A & 5 & 4 & 7 \\
\hline B & 4 & 6 & 4 \\
\hline
\end{tabular}

Steve needs to take at least 24 milligrams of calcium, 15 milligrams of iron, and 16 milligrams of vitamins. Which ordered pairs of values are solutions for the given system of inequalities, where [tex]$x$[/tex] represents the number of spoonfuls of Brand A that Steve takes and [tex]$y$[/tex] represents the number of spoonfuls of Brand B that Steve takes?

Select all the correct answers.

A. (1, 4)

B. (1, 5)

C. [tex][tex]$(2, 3)$[/tex][/tex]

D. [tex]$(3, 2)$[/tex]

E. (4, 1)

Sagot :

GinnyAnsweridn
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)
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