Correct Answer:
A. 5
The correct answer is 5. A ratio expresses the proportional relationship between parts of a whole. In the given ratio 1 : x : 5, the three parts are represented by 1, x, and 5 respectively. Since the problem states that their total sum equals 11, we can directly translate this into a simple algebraic equation.
Solving the Equation Step by Step
- Form the equation: The sum of the ratio parts is 1 + x + 5. We set this equal to 11:
- 1 + x + 5 = 11
- Combine the known numbers: Add 1 and 5 to get 6. The equation simplifies to:
- x + 6 = 11
- Isolate the variable: Subtract 6 from both sides of the equation to solve for x:
- x = 11 − 6
- x = 5
Thus, the missing term in the ratio is 5, making the complete ratio 1 : 5 : 5. A quick verification confirms our solution: 1 + 5 + 5 = 11, which perfectly matches the given sum.
Why the Other Options Are Incorrect
- Option 2 (6): If x = 6, the sum would be 1 + 6 + 5 = 12, which is greater than 11.
- Option 3 (7): If x = 7, the sum would be 1 + 7 + 5 = 13, which does not match.
- Option 4 (8): If x = 8, the sum would be 1 + 8 + 5 = 14, again incorrect.
Hence, the only value that satisfies the condition is x = 5, which corresponds to Option 1.