23% of 8040 + 42% of 545 = $x$% of 3000

### Concept & Logic This requires evaluating the sum of two separate percentage expressions and then determining what percentage that total sum represents out of a new base number (3000). $$ \text{Total Sum} = \left(\frac{x}{100}\right) \times \text{Base} $$ ### Step-by-Step Solution * **Given:** Equation: 23% of 8040 + 42% of 545 = $x$% of 3000 * **Calculation:** Step 1: Evaluate the first term (23% of 8040). $ 0.23 \times 8040 = 1849.2 $ Step 2: Evaluate the second term (42% of 545). $ 0.42 \times 545 = 228.9 $ Step 3: Add the two terms together to find the total sum. $ 1849.2 + 228.9 = 2078.1 $ Step 4: Set up the final equation and solve for $x$. $ 2078.1 = x\% \text{ of } 3000 $ $ 2078.1 = \left(\frac{x}{100}\right) \times 3000 $ $ 2078.1 = 30x $ $ x = \frac{2078.1}{30} = 69.27 $ ### Exam Strategy & Shortcut Break down complex percentages into easier chunks. For 23% of 8040: Find 20% (double 10%, so $ 804 \times 2 = 1608 $). Then find 3% ($ 80.4 \times 3 = 241.2 $). Sum them: $ 1608 + 241.2 = 1849.2 $. For 42% of 545: Find 40% ($ 54.5 \times 4 = 218 $). Then find 2% ($ 5.45 \times 2 = 10.9 $). Sum them: $ 218 + 10.9 = 228.9 $. Add the two results: $ 1849.2 + 228.9 = 2078.1 $. Divide by 30 to get $x$. The arithmetic is much safer and faster using this additive chunking method. ### Common Pitfall Because the final equation is $ 2078.1 = 30x $, students often mistakenly divide by 3000 instead of 30, forgetting that the percentage sign on $x$ already canceled out two zeros from the 3000. ### Final Answer **Therefore, the correct answer is 69.27.**