$853 + x \div 17 = 1000$

Concept & Logic This is a fundamental algebraic equation. To isolate the unknown variable $x$, you must reverse the order of operations, peeling away the constants on the left side by moving them to the right side of the equals sign. Step-by-Step Solution * Given equation: $$ 853 + \frac{x}{17} = 1000 $$ * Step 1: Isolate the fraction containing $x$ by subtracting $853$ from both sides. $$ \frac{x}{17} = 1000 - 853 $$ $$ \frac{x}{17} = 147 $$ * Step 2: Solve for $x$ by multiplying both sides by $17$. $$ x = 147 \times 17 $$ * Step 3: Perform the multiplication. You can break $17$ into $(10 + 7)$ for easier mental math. $$ x = 147 \times (10 + 7) $$ $$ x = 1470 + 1029 $$ $$ x = 2499 $$ Exam Strategy & Shortcut **Unit Digit Verification:** Once you reach the step $x = 147 \times 17$, you do not need to calculate the entire product. Simply multiply the unit digits of the two numbers: $7 \times 7 = 49$. The final product must have a unit digit of $9$. Looking closely at the given options, only option (b) 2499 ends in a $9$. You can confidently select this option and save precious seconds. Common Pitfall A very common error is misinterpreting the BODMAS rule and attempting to add $853$ directly to $x$ before dealing with the division, mistakenly writing $\frac{(853 + x)}{17} = 1000$. This leads to $853 + x = 17000$, resulting in $x = 16147$, which is entirely incorrect (and cleverly placed as option d). Final Answer **Therefore, the correct answer is 2499.**