The product of two numbers is 9375, and the quotient (larger ÷ smaller) is 15. What is the sum of the two numbers?

Problem restatementLet the smaller number be x and the larger be 15x. Given their product equals 9375; find x and hence their sum.

Concept/ApproachUse product and ratio to form an equation in one variable.

Step-by-Step calculation(15x) × x = 9375 ⇒ 15x² = 9375x² = 9375 ÷ 15 = 625 ⇒ x = 25 (positive)Larger = 15x = 375Sum = 25 + 375 = 400

Verification/AlternativeProduct check: 25 × 375 = 9375. Quotient: 375 ÷ 25 = 15.

Common pitfallsTaking square root as −25 (numbers are positive in this context) or mixing which is larger.

Final Answer400