A number when divided by 47 gives a quotient of 75 and a remainder of 18. What is this original number?

Introduction / Context:
This is a direct application of the division algorithm. You are given the divisor, quotient, and remainder, and you must reconstruct the original number. Such problems test understanding of the basic relationship between these four quantities.

Given Data / Assumptions:
- Divisor = 47.
- Quotient = 75.
- Remainder = 18.
- We are asked to find the original number that satisfies these values.

Concept / Approach:
The division algorithm states that for any integers dividend, divisor, quotient, and remainder, the relation dividend = divisor * quotient + remainder holds, with remainder less than divisor. Here, we simply substitute the given values into this expression.

Step-by-Step Solution:
Step 1: Use the formula dividend = divisor * quotient + remainder.Step 2: Substitute divisor = 47, quotient = 75, and remainder = 18.Step 3: Compute 47 * 75 first. 47 * 75 = 47 * (3 * 25) = 141 * 25 = 3525.Step 4: Add the remainder: 3525 + 18 = 3543.Step 5: So the original number is 3543.

Verification / Alternative check:
Verify by performing the division in reverse. Divide 3543 by 47. The quotient is 75 because 47 * 75 = 3525. The difference between 3543 and 3525 is 18, which is the remainder. Since the remainder 18 is less than the divisor 47, this fits the division algorithm correctly, confirming that 3543 is the correct original number.

Why Other Options Are Wrong:
For 3507, dividing by 47 gives 47 * 74 = 3478 with remainder 29, not 18. For 3489, 47 * 74 = 3478 with remainder 11. For 3561, 47 * 75 = 3525 with remainder 36. Option 3609 is even further away, producing a different quotient and remainder. Only 3543 matches the required quotient of 75 and remainder of 18.

Common Pitfalls:
Students sometimes reverse roles of quotient and remainder or forget the formula dividend = divisor * quotient + remainder. Others may multiply incorrectly or add the remainder to the wrong intermediate value. Careful arithmetic is essential because a small multiplication error yields a completely different answer.

Final Answer:
The original number that gives quotient 75 and remainder 18 when divided by 47 is 3543.