This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Define the variables and set up the equations. Let the two numbers be x and y. Assume x is the larger number and y is the smaller number. From the problem statement, we have two conditions: 1. The product of the two numbers is 6250: x · y = 6250 (1) 2. The quotient when the larger number is divided by the smaller number is 10: (x)/(y) = 10 (2) Step 2: Express one variable in terms of the other. From equation (2), we can express x in terms of y: x = 10y Step 3: Substitute the expression for x into equation (1). Substitute x = 10y into x · y = 6250: (10y) · y = 6250 10y^2 = 6250 Step 4: Solve for y. Divide both sides by 10: y^2 = (6250)/(10) y^2 = 625 Take the square root of both sides: y = sqrt(625) y = 25 Step 5: Solve for x. Substitute the value of y back into x = 10y: x = 10 · 25 x = 250 Step 6: Find the sum of the numbers. The sum of the numbers is x + y: Sum = 250 + 25 Sum = 275 The correct option is (c). The final answer is 275. 3 done, 2 left today. You're making progress.