Question

the sum of two numbers is no more than 28. let x represent the first number, and let y represent the second number. which inequality represents this situation?
○ y < x + 28y
○ y ≤ x + 28
○ x + y < 28
○ x + y ≤ 28

Explanation:

Step1: Understand the problem

We need to translate the statement "The sum of two numbers is no more than 28" into an inequality. Let \( x \) be the first number and \( y \) be the second number. The sum of the two numbers is \( x + y \).

Step2: Interpret "no more than"

The phrase "no more than" means that the sum \( x + y \) is less than or equal to 28. In mathematical notation, this is written as \( x + y \leq 28 \).

Step3: Analyze the options

• Option 1: \( y < x + 28y \) does not represent the sum of two numbers being no more than 28.
• Option 2: \( y \leq x + 28 \) represents a relationship between \( y \), \( x \), and 28, not the sum of \( x \) and \( y \) being no more than 28.
• Option 3: \( x + y < 28 \) means the sum is less than 28, but "no more than" includes equality, so this is incorrect.
• Option 4: \( x + y \leq 28 \) correctly represents the sum of \( x \) and \( y \) being less than or equal to 28 (i.e., no more than 28).

Answer:

D. \( x + y \leq 28 \) (assuming the last option is D, if the options are labeled as such; if the last option is the fourth one with the inequality \( x + y \leq 28 \), then that is the correct option)