Error analysis with fractions: A student was asked to multiply a number by 3/2 but instead divided the number by 3/2 (i.e., multiplied by 2/3). The result was 10 less than the correct result. Find the original number.

Introduction / Context:
This problem focuses on comparing the intended operation with the erroneous one. By modeling both results in algebra and equating their difference to 10, we can solve directly for the original number without guesswork.

Given Data / Assumptions:

• Correct operation: multiply by 3/2.
• Actual operation: divide by 3/2, equivalent to multiply by 2/3.
• Wrong result is 10 less than the correct result.

Concept / Approach:
Let the original number be x. Then correct result is (3/2)*x, and wrong result is (2/3)*x. Their difference is specified, so form an equation and solve for x. Keep fractions exact to avoid rounding errors.

Step-by-Step Solution:
Let correct − wrong = 10 → (3/2)x − (2/3)x = 10.Compute the coefficient: 3/2 − 2/3 = 9/6 − 4/6 = 5/6.Thus (5/6)x = 10.Solve: x = 10 * (6/5) = 12.

Verification / Alternative check:
Correct result for x = 12 is (3/2)*12 = 18; wrong result is (2/3)*12 = 8; difference = 10, consistent with the statement.

Why Other Options Are Wrong:
10, 15, and 20 do not satisfy the setup; “None of these” is unnecessary since 12 is exact.

Common Pitfalls:
Adding rather than subtracting the expressions; flipping 3/2 incorrectly; arithmetic slips when working with fractions.

Final Answer:
12