In a division sum, the divisor is 9 times the quotient and 3 times the…

Concept

The division algorithm states: dividend = divisor × quotient + remainder.

The remainder must be smaller than the divisor, and relationships among divisor, quotient, and remainder can be translated into equations.

Application

1. Let the remainder be r = 18.

2. The divisor is 3 times the remainder, so divisor = 3 × 18 = 54.

3. The divisor is 9 times the quotient, so quotient = 54 ÷ 9 = 6.

4. Using the division algorithm, dividend = 54 × 6 + 18 = 324 + 18 = 342.

Cross-check

Dividing 342 by 54 gives quotient 6 and remainder 18. Also, 54 = 9 × 6 and 54 = 3 × 18, so every stated relationship is satisfied.

Therefore, the dividend is 342.