Question

P, Q and R are three consecutive odd numbers in ascending order. If the value of three times P is 3 less than two times R, find the value of R?

• A. 7
• B. 11
• C. 33
• D. 9
• E. 5

Hint:

Represent consecutive odd numbers as $x, x+2, x+4$ and set up the equation.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Consecutive odd numbers have a difference of 2 between them.
Step 2: Key Formula or Approach:
Let \(P = x\). Then \(Q = x + 2\) and \(R = x + 4\). Equation: \(3P = 2R - 3\).
Step 3: Detailed Explanation:
1. Substitute the variables into the equation: \[ 3x = 2(x + 4) - 3 \] 2. Simplify: \[ 3x = 2x + 8 - 3 \] \[ 3x = 2x + 5 \] \[ x = 5 \] 3. Find R: \[ R = x + 4 = 5 + 4 = 9 \].
Step 4: Final Answer:
The value of R is 9.