Solve for the missing value in a rational equation: Find ? such that (20 + 8 × 0.5) / (20 − ?) = 12.
Aptitude
Decimal Fraction
Difficulty: Easy
Choose an option
-
A8
-
B18
-
C2
-
DNone these
Answer
Correct Answer: 18
Explanation
Introduction / Context:This item assesses linear equation solving with decimals inside a fraction. The key is to simplify the numerator first, then isolate the denominator expression and solve for the unknown while preserving equality.
Given Data / Assumptions:
- (20 + 8 × 0.5) / (20 − x) = 12
- All arithmetic is exact; no rounding required.
Concept / Approach:Compute the numerator cleanly. Then, cross-multiply (since the denominator is nonzero) to solve for x. Check that the solution does not make the denominator zero and that it satisfies the original equation.
Step-by-Step Solution:
Compute numerator: 8 × 0.5 = 4, so 20 + 4 = 24Equation: 24 / (20 − x) = 12Invert both sides: 20 − x = 24 / 12 = 2x = 20 − 2 = 18Verification / Alternative check:
Plug back: (20 + 4) / (20 − 18) = 24 / 2 = 12 ✔Why Other Options Are Wrong:
- 8 or 2: Do not satisfy 24 / (20 − x) = 12.
- None these: Not applicable because x = 18 works exactly.
Common Pitfalls:
- Forgetting to simplify the numerator before solving.
- Arithmetic slips when subtracting from 20.
Final Answer:
18