Final answer:
To find the sum of the two numbers, set up equations using the given information and solve for the numbers. The sum of the two numbers is 400.
Step-by-step explanation:
To find the sum of the two numbers, we need to first find the two numbers. Let's call the larger number x and the smaller number y. We know that the product of the two numbers is 9375, so xy = 9375. We also know that the quotient when the larger number is divided by the smaller number is 15, so x/y = 15. From these two equations, we can solve for x and y.
Step 1: From xy = 9375, we can choose two factors of 9375 such that their difference is 15. Let's try 75 and 125: 75 * 125 = 9375.
Step 2: Since x/y = 15, we can set up the equation x = 15y and substitute it into the equation xy = 9375. We get (15y)y = 9375, which simplifies to 15y^2 = 9375. Divide both sides by 15 to get y^2 = 625. Taking the square root of both sides, we get y = 25.
Step 3: Substitute the value of y back into x = 15y. We get x = 15 * 25 = 375.
Finally, we can find the sum of the two numbers: x + y = 375 + 25 = 400. Therefore, the sum of these two numbers is 400.