In a question of division, the divisor is 9 times the quotient and 5 times the…

Concept: The division algorithm states that for any division: Dividend = (Divisor × Quotient) + Remainder. When the divisor is described as a multiple of the remainder and also a multiple of the quotient, first recover the divisor from the remainder relation, then recover the quotient from the divisor relation, and only then apply the identity above.

Application:

1. Divisor = 5 × Remainder = 5 × 45 = 225

2. Quotient = Divisor ÷ 9 = 225 ÷ 9 = 25

3. Dividend = (Divisor × Quotient) + Remainder = (225 × 25) + 45 = 5670

Cross-check: Cross-check: dividing 5670 by 225 gives a quotient of 25 with a remainder of 45 — exactly the quotient and remainder used above, and 225 is indeed 5 times 45 and 9 times 25, so every given relation is satisfied.