In a division operation, the divisor equals ten times the quotient and also equals five times the remainder. If the remainder is 46, find the dividend.

Introduction / Context:This problem connects the four elements of a division algorithm: dividend, divisor, quotient, and remainder. Using the given proportional relationships, you can determine the divisor and quotient, then reconstruct the dividend through the standard identity Dividend = Divisor * Quotient + Remainder.

Given Data / Assumptions:

• Remainder R = 46.
• Divisor D = 5 * R.
• Divisor D = 10 * Quotient Q.
• Division identity: Dividend N = D * Q + R.

Concept / Approach:First compute D from the remainder. Then use D = 10Q to find Q. Finally, apply N = DQ + R. This sequence avoids guesswork and keeps arithmetic simple and exact.

Step-by-Step Solution:

Verification / Alternative check:Check proportions: D = 230 is five times 46 and ten times 23. Substituting into N = DQ + R reproduces the given remainder exactly.

Why Other Options Are Wrong:5388, 5343, 5391, and 5328 do not satisfy the division identity with D = 230, Q = 23, and R = 46.

Common Pitfalls:Confusing which term is 10 times which (mistaking Q = 10D), or omitting the remainder when reconstructing the dividend.

Final Answer:5336