Final answer:
To find the larger of two numbers with a given arithmetic mean and product, set up equations based on the mean and the square root of the product. Solve these simultaneous equations to find the larger number, which in this case is 20.
Step-by-step explanation:
The student is asking to find the larger of two numbers where the arithmetic mean is 18 3/4 and the positive square root of their product is 15. To solve this, we can set up two equations based on the given information:
- The sum of the two numbers divided by 2 (since it's the mean of two numbers) is equal to 18 3/4.
- The positive square root of their product is equal to 15.
Let's denote the two numbers as x (the larger number) and y (the smaller number). Then we have:
- (x + y) / 2 = 18 3/4
- sqrt(x * y) = 15
From the second equation, we know that x * y = 15^2 = 225. From the first equation, we can express y in terms of x: y = 2(18 3/4) - x = 37.5 - x. Now we can substitute for y in the product equation: x * (37.5 - x) = 225. Solving for x gives us two possible solutions, but since x is the larger number, we identify the correct solution as x = 20. Thus, the answer is (a) 20.