$140\%$ of $56 + 56\%$ of $140 = $x$

### Concept & Formula The commutative property of percentages dictates that swapping the percentage value and the base number does not change the result. $$ a\% \text{ of } b = b\% \text{ of } a $$ ### Step-by-Step Solution * **Given:** The expression is $140\%$ of $56 + 56\%$ of $140$. * **Calculation:** Apply the commutative property to rewrite the second term. $$ 56\% \text{ of } 140 \text{ is identical to } 140\% \text{ of } 56 $$ * The equation simplifies to: $$ 140\% \text{ of } 56 + 140\% \text{ of } 56 = 2 \times (140\% \text{ of } 56) $$ * Calculate $140\%$ of $56$. $$ 1.4 \times 56 = 78.4 $$ * Multiply by 2. $$ 2 \times 78.4 = 156.8 $$ * Comparing this to the given options, $156.8$ is not listed. ### Exam Strategy & Shortcut Whenever you see a pattern like $A\%$ of $B + B\%$ of $A$, immediately translate it to $2 \times (A\%$ of $B)$. Calculate $1.4 \times 56$ as $(1 + 0.4) \times 56 = 56 + 22.4 = 78.4$. Double it to get $156.8$. This removes the need to calculate two separate, seemingly different percentages. ### Common Pitfall Calculating only the first half ($140\%$ of $56 = 78.4$) and eagerly selecting option (a) $78.4$, completely forgetting to add the second equivalent term. ### Final Answer **Therefore, the correct answer is None of these.**