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

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

Concept/Approach
Use 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/Alternative
Product check: 25 × 375 = 9375. Quotient: 375 ÷ 25 = 15.

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

Final Answer
400