Evaluate the expression 30 + (0.0825 × 30) + (15% × 30), giving the final result as a decimal number.

Introduction / Context:
This question is a straightforward numerical calculation involving decimals and percentages applied to the same base number. Such questions are used to test basic numerical manipulation skills including conversion between percentages and decimal multipliers and accurate arithmetic operations.

Given Data / Assumptions:

The expression to evaluate is 30 + (0.0825 × 30) + (15% × 30).

All multiplications and additions are done using normal arithmetic rules.

15% means 15 / 100 as a fraction or 0.15 as a decimal multiplier.

Concept / Approach:
The approach is to compute each term step by step. First compute 0.0825 × 30. Then compute 15% of 30, which is 0.15 × 30. Finally, add these two results to 30. The main idea is to understand that percentages can always be converted into decimal form before multiplication, which often makes calculations easier and clearer.

Step-by-Step Solution:
Step 1: Compute 0.0825 × 30.0.0825 × 30 = 2.475.Step 2: Convert 15% to decimal and multiply by 30.15% = 15 / 100 = 0.15, so 0.15 × 30 = 4.5.Step 3: Now add all three terms in the expression.30 + 2.475 + 4.5 = 36.975.Step 4: Therefore the value of the expression is 36.975.

Verification / Alternative check:
You can factor 30 from each term to check quickly: 30 + 0.0825 × 30 + 0.15 × 30 = 30 × (1 + 0.0825 + 0.15) = 30 × 1.2325. Now multiply 30 × 1.2325 = 36.975, which agrees with the earlier calculation. This confirms that no arithmetic error has occurred.

Why Other Options Are Wrong:
24.750 is roughly the value of 30 minus a percentage, not plus two percentage based increments.
34.652 and 26.354 are arbitrary looking decimals and do not result from any correct combination of the given terms.
32.475 ignores part of the increase from the percentage components and is smaller than the true sum.

Common Pitfalls:
A frequent mistake is misreading 0.0825 as 0.825 or 0.00825, which drastically changes the product. Another common error is to treat 15% of 30 as 15 / 30 instead of 15 / 100 × 30. Students also sometimes forget to add all terms correctly or mishandle decimal addition. Writing each step clearly and aligning decimal points during addition helps avoid such errors.

Final Answer:
The value of the expression is 36.975.