Problem
10 The recommended daily calcium intake for a 20-year-old person is 1,000 milligrams (mg). One cup of milk contains $299 \mathrm{mg}$ of calcium and one cup of juice contains $261 \mathrm{mg}$ of calcium. Which of the following inequalities represents the possible number of cups of milk, $m$, and cups of juice, $j$, a 20-year-old person could drink in a day to meet or exceed the recommended daily calcium intake from these drinks alone? A) $299 m+261 j \geq 1,000$ B) $299 m+261 j>1,000$ C) $\frac{299}{m}+\frac{261}{j} \geq 1,000$ D) $\frac{299}{m}+\frac{261}{j}>1,000$ Content: Heart of Algebra Key: A Objective: You must identify the correct mathematical notation for an inequality to represent a real-world situation.
Solution
Step 1 ：Let m be the number of cups of milk and j be the number of cups of juice. The total calcium intake can be represented as \(299m + 261j\).
Step 2 ：We need to find the inequality that represents the total calcium intake being greater than or equal to 1000 mg.
Step 3 ：\(299m + 261j \geq 1000\)
Step 4 ：\(\boxed{299m + 261j \geq 1000}\)
