In the expression 63.5% of 8924.2 plus x% of 5324.4 equals 6827.5862, what is the value of x (in percent)?

Introduction / Context:
This question asks you to find an unknown percentage in a linear equation involving percentages. One term of the expression is a known percentage of a given number, and the second term is an unknown percentage of another number. Their sum is equal to a specified total. This is a typical algebraic percentage problem where we convert percentage phrases into algebraic expressions and then solve for the unknown percentage.

Given Data / Assumptions:

• We have 63.5% of 8924.2 plus x% of 5324.4 equals 6827.5862.
• That is, 63.5% of 8924.2 + x% of 5324.4 = 6827.5862.
• We must determine the value of x (the unknown percentage) in whole percent, matching the nearest option.

Concept / Approach:
The phrase “63.5% of 8924.2” translates to 0.635 * 8924.2, and “x% of 5324.4” translates to (x / 100) * 5324.4. We first compute the known term 0.635 * 8924.2, then subtract that from 6827.5862 to isolate the unknown term. After that, we divide by 5324.4 and multiply by 100 to find x as a percentage. Finally, we compare the result to the given options and choose the closest match.

Step-by-Step Solution:
Step 1: Compute the known percentage term. 63.5% of 8924.2 = 0.635 * 8924.2. 0.635 * 8924.2 ≈ 5666.867. Step 2: Use the given equation. 5666.867 + (x / 100) * 5324.4 = 6827.5862. Step 3: Subtract 5666.867 from both sides to isolate the unknown term. (x / 100) * 5324.4 = 6827.5862 - 5666.867. Step 4: Compute the right side: 6827.5862 - 5666.867 ≈ 1160.7192. Step 5: Now (x / 100) * 5324.4 ≈ 1160.7192. Step 6: Solve for x / 100: (x / 100) = 1160.7192 / 5324.4. Step 7: Compute 1160.7192 / 5324.4 ≈ 0.218, that is 21.8%. Step 8: Thus x ≈ 21.8. The nearest integer percentage among the options is 22.

Verification / Alternative check:
Take x = 22% and recompute the total. 22% of 5324.4 = 0.22 * 5324.4 ≈ 1171.368. Add the earlier term 5666.867: 5666.867 + 1171.368 ≈ 6838.235. This is reasonably close to 6827.5862, and the small difference can be attributed to rounding issues in intermediate steps and the approximate nature of the given decimal values. Given the answer choices, 22% fits best with the computed approximate value of 21.8%.

Why Other Options Are Wrong:
If x were 28%, the second term would be much larger and the total would exceed the target value significantly. Similarly, 18% or 12% would yield totals that are too small. Only 22% is close to the mathematically derived approximate value of 21.8%, making it the correct choice from the provided options.

Common Pitfalls:
One common mistake is to confuse percentage points with percentage values, or to misplace the decimal when converting from percent to a decimal factor. Another pitfall is to round intermediate results too early, which can cause noticeable discrepancies when recomputed. It is advisable to keep several decimal places in calculations until the final step and then match the result to the closest option.

Final Answer:
The value of x is approximately 22%.