$341.42 - 53.74 = $ $x$ $- 62.86$

### Concept & Formula To find the value of the unknown variable $x$, isolate it on one side of the equation by shifting terms across the equals sign. Remember that moving a negative term changes its sign to positive. $$ a - b = x - c \implies x = a - b + c $$ ### Step-by-Step Solution * Write down the initial algebraic equation: * $341.42 - 53.74 = x - 62.86$ * Rearrange the equation to isolate $x$: * $x = 341.42 - 53.74 + 62.86$ * According to BODMAS/order of operations, group the positive values together before subtracting: * $x = (341.42 + 62.86) - 53.74$ * Perform the addition: * $341.42 + 62.86 = 404.28$ * Perform the final subtraction: * $404.28 - 53.74 = 350.54$ * Comparing this result to the given options, $350.54$ matches option (c). However, let's verify the options. Wait, option (c) is listed exactly as $350.54$. Let's re-read the option array: (a) $260.44$, (b) $340.44$, (c) $350.54$, (d) $450.54$. So option (c) is the exact match. ### Exam Strategy & Shortcut **Unit Digit Check:** Let's evaluate the terminal digit trends: $x \equiv 2 - 4 + 6 \pmod{10}$ $2 - 4 = -2 \rightarrow 8$. $8 + 6 = 14 \rightarrow$ ends in $.54$ or $.04$ depending on tenths carry. Let's evaluate hundredths place explicitly: $.42 - .74 + .86 = -.32 + .86 = .54$. The exact value must end in $.54$. This narrows your targets exclusively down to options (c) and (d). A quick look at the integer components ($341 - 53 + 62 \approx 350$) confirms option (c) immediately. ### Common Pitfall Students often make mistakes by subtracting $62.86$ from $53.74$ first due to positional confusion rather than accurately following algebraic transposition rules. ### Final Answer **Therefore, the correct answer is $350.54$.**