Evaluate the expression 21% of 500 plus 31% of 1100 minus 30% of 790. What is the value of this numerical expression?

Introduction / Context:
This is a direct numerical computation involving multiple percentages applied to different numbers. Problems like this measure comfort with converting percentage expressions into arithmetic operations and performing accurate calculations. There is no tricky conceptual twist; accuracy and systematic working are the main skills required.

Given Data / Assumptions:

• We must compute: 21% of 500 + 31% of 1100 - 30% of 790.
• Percent means “per hundred”, so x% of y is (x / 100) * y.
• All numbers are in standard units; no special units are attached.

Concept / Approach:
The approach is to handle each percentage piece separately. First, convert each percentage to its decimal form (for example, 21% becomes 0.21). Then multiply it with the corresponding base number. After obtaining the three numeric values, add the first two results and subtract the third as indicated. Keeping calculations neat and stepwise helps avoid simple arithmetic errors.

Step-by-Step Solution:
Step 1: Compute 21% of 500. 21% of 500 = (21 / 100) * 500 = 0.21 * 500. 0.21 * 500 = 105. Step 2: Compute 31% of 1100. 31% of 1100 = (31 / 100) * 1100 = 0.31 * 1100. 0.31 * 1100 = 341. Step 3: Compute 30% of 790. 30% of 790 = (30 / 100) * 790 = 0.30 * 790. 0.30 * 790 = 237. Step 4: Combine the results: 21% of 500 + 31% of 1100 - 30% of 790 = 105 + 341 - 237. Step 5: 105 + 341 = 446. Step 6: 446 - 237 = 209. Step 7: Therefore, the final value of the expression is 209.

Verification / Alternative check:
We can quickly cross check using approximate mental arithmetic. 20% of 500 is around 100, so 21% should be slightly more than 100; 31% of 1100 is around one third, about 360, but exactly 341; and 30% of 790 is roughly 240. Then 100 plus 340 minus 240 is close to 200. This sanity check supports the precise calculation of 209, as it lies within the expected range.

Why Other Options Are Wrong:
290 and 309 are higher than the result we got and would require either an error in one of the percentage multiplications or incorrect addition and subtraction. 390 is far too large and would correspond to neglecting the subtraction term almost entirely. Careful calculation clearly produces 209 as the only correct value.

Common Pitfalls:
Students may forget to divide by 100 when converting percentages, effectively treating 21% of 500 as 21 * 500 instead of 0.21 * 500. Another common mistake is mixing up the order of operations or incorrectly subtracting the final term. Writing each intermediate result clearly and performing arithmetic in a stepwise fashion significantly reduces these risks.

Final Answer:
The value of the expression is 209.