The recommended daily calcium intake for a 20-year-old is 1,000 milligrams (mg). One cup of milk contains 299 mg of calcium and one cup of juice contains 261 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 could drink in a day to meet or exceed the recommended daily calcium intake from these drinks alone?

  • A. 299m + 261j >= 1000
  • B. 299m + 261j > 1000
  • C. 299/m + 361/j >= 1000
  • D. 299/m + 361/j > 1000

Answer: A

Why?

Multiplying the number of cups of milk by the amount of calcium each cup contains and multiplying the number of cups of juice by the amount of calcium each cup contains gives the total amount of calcium from each source. The student must then find the sum of these two numbers to find the total amount of calcium. Because the question asks for the calcium from these two sources to meet or exceed the recommended daily intake, the sum of these two products must be greater than or equal to 1,000.

Question Difficulty: EASY

Objective: Students must identify the correct mathematical notation for an inequality to represent a real-world situation.

Words:
  1. calcium – canxi  (n): the chemical element of atomic number 20, a soft gray metal.
  2. intake – lượng (n): an amount of food, air, or another substance taken into the body.
  3. inequality (n): bất đẳng thức.
  4. exceed – vượt quá (v): be greater in number or size than (a quantity, number, or other measurable thing).
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