Find the unknown number.
If half of a number is added to $\frac{2}{5}$, the result is the same as subtracting $\frac{1}{10}$ from the number.

• A. $-\frac{1}{5}$
• B. $-1$
• C. $1$
• D. $-\frac{3}{5}$

Answer: (C)

Verified step by step guidance

1. Let the unknown number be represented by the variable \(x\).
2. Translate the problem statement into an equation: "If half of a number is added to two fifths, the result is the same as subtracting one tenth from the number." This can be written as: \(\frac{1}{2}x + \frac{2}{5} = x - \frac{1}{10}\).
3. To solve for \(x\), first eliminate the fractions by finding the least common denominator (LCD) of 2, 5, and 10, which is 10. Multiply every term in the equation by 10 to clear the denominators: \(10 \times \left(\frac{1}{2}x + \frac{2}{5}\right) = 10 \times \left(x - \frac{1}{10}\right)\).
4. Simplify both sides after multiplying: \(10 \times \frac{1}{2}x = 5x\), \(10 \times \frac{2}{5} = 4\), \(10 \times x = 10x\), and \(10 \times \frac{1}{10} = 1\). So the equation becomes \$5x + 4 = 10x - 1$.
5. Next, isolate the variable \(x\) by moving all \(x\) terms to one side and constants to the other: subtract \$5x\( from both sides and add \)1\( to both sides to get \)4 + 1 = 10x - 5x\(, which simplifies to \)5 = 5x\(. Then, divide both sides by 5 to solve for \)x$.