Question:
When \(2\frac{1}{2}\) is added to a number and the sum is multiplied by \(4\frac{1}{2}\) and then 3 is added to the product and then the sum is divided by \(1\frac{1}{5}\), the quotient becomes 25. What is that number?
When \(2\frac{1}{2}\) is added to a number and the sum is multiplied by \(4\frac{1}{2}\) and then 3 is added to the product and then the sum is divided by \(1\frac{1}{5}\), the quotient becomes 25. What is that number?
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Translate each operation step-by-step into algebra and solve backwards. Convert mixed fractions into improper forms for simplification.
Updated On: Aug 7, 2025
- \(2\frac{1}{2}\)
- \(3\frac{1}{2}\)
- \(4\frac{1}{2}\)
- \(5\frac{1}{2}\)
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The Correct Option is B
Solution and Explanation
Let the number be \( x \).
Then:
\[
\text{Step 1: } x + \frac{5}{2}
\text{Step 2: } \left(x + \frac{5}{2}\right) \times \frac{9}{2}
\text{Step 3: } \left[ \left(x + \frac{5}{2}\right) \cdot \frac{9}{2} \right] + 3
\text{Step 4: } \frac{\left[\left(x + \frac{5}{2}\right) \cdot \frac{9}{2} + 3\right]}{\frac{6}{5}} = 25 \] Now solve: \[ \left[\left(x + \frac{5}{2}\right) \cdot \frac{9}{2} + 3\right] = 25 \cdot \frac{6}{5} = 30 \] \[ \left(x + \frac{5}{2}\right) \cdot \frac{9}{2} = 27 \Rightarrow x + \frac{5}{2} = \frac{27 \cdot 2}{9} = 6 \Rightarrow x = 6 - \frac{5}{2} = \frac{7}{2} = \boxed{3\frac{1}{2}} \] \fbox{Final Answer: (B) \(3\frac{1}{2}\)}
\text{Step 2: } \left(x + \frac{5}{2}\right) \times \frac{9}{2}
\text{Step 3: } \left[ \left(x + \frac{5}{2}\right) \cdot \frac{9}{2} \right] + 3
\text{Step 4: } \frac{\left[\left(x + \frac{5}{2}\right) \cdot \frac{9}{2} + 3\right]}{\frac{6}{5}} = 25 \] Now solve: \[ \left[\left(x + \frac{5}{2}\right) \cdot \frac{9}{2} + 3\right] = 25 \cdot \frac{6}{5} = 30 \] \[ \left(x + \frac{5}{2}\right) \cdot \frac{9}{2} = 27 \Rightarrow x + \frac{5}{2} = \frac{27 \cdot 2}{9} = 6 \Rightarrow x = 6 - \frac{5}{2} = \frac{7}{2} = \boxed{3\frac{1}{2}} \] \fbox{Final Answer: (B) \(3\frac{1}{2}\)}
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