Final answer:
The Geometric Mean (GM) when the Arithmetic Mean (AM) is 28 and the ratio of AM to GM is 4:3 is found to be 21.
Step-by-step explanation:
The student is asking about finding the Geometric Mean (GM) when given the Arithmetic Mean (AM) and a ratio of AM to GM of two numbers. Here is the step-by-step explanation: The ratio of AM to GM is 4:3, and the AM is 28. The formula that connects AM, GM, and the two numbers in question is AM = (x + y)/2 and GM = √(xy), where x and y are the numbers.
First, express the given AM ratio in terms of x and y:
AM/GM = (x + y) / 2√(xy) = 4/3. As AM is given as 28, we can plug this into the equation: 28/GM = 4/3. Cross-multiply to find GM: 3 × 28 = 4 × GM, which simplifies to GM = (3 × 28) / 4 = 21.