Question

If x and y are positive integers, what percent of three more than y is twice the value of x?

• A. 1/200x(y + 3)
• B. y + 3/200x
• C. 100(y + 3)/2x
• D. (200x/y) + 3
• E. 200x/(y + 3)

Hint:

In percentage word problems, the number or expression that follows the word "of" is almost always the denominator (the "whole" or "base") in the percentage calculation.

Answer 1

Answer: (E)

Step 1: Understanding the Concept:
This is a word problem that requires translating a sentence into a mathematical expression for percentage. The key is to correctly identify the "part" and the "whole" (or base) in the percentage relationship.

Step 2: Key Formula or Approach:
The general formula for percentage is: \[ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \] The phrase "what percent of A is B" translates to: \[ \text{Percentage} = \left( \frac{B}{A} \right) \times 100 \] Here, A is the "whole" or the base, and B is the "part".

Step 3: Detailed Explanation:
Let's break down the sentence: "what percent of three more than y is twice the value of x?"
\[\begin{array}{rl} \bullet & \text{The quantity that follows "of" is the base or the "whole". So, Whole = "three more than y" = \(y + 3\).} \\ \bullet & \text{The quantity being compared to the base is the "part". So, Part = "twice the value of x" = \(2x\).} \\ \end{array}\] Now, we plug these into the percentage formula: \[ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \] \[ \text{Percentage} = \left( \frac{2x}{y + 3} \right) \times 100 \] Simplifying this expression gives: \[ \text{Percentage} = \frac{200x}{y + 3} \] This matches option (E).
Step 4: Final Answer
The expression representing the percentage is \( \frac{200x}{y + 3} \).