Final answer:
Solve for individual values of x, y, z, and w using their given ratios, then substitute those into the expression xyw/z to find the final value.
Step-by-step explanation:
The question at hand requires us to solve a series of ratios to find the value of xyw/z. Given the ratios x/y = 4/5, y/z = 3/10, and z/w = 6/7, we can first find the individual values of x, y, z, and w by assuming a common variable, then solve for xyw/z.
To solve these ratios, let's assume z to be a value that makes the calculations simple, such as 70 (since it is a multiple of both 10 and 7). With z = 70, we can calculate y from the second ratio (y/z = 3/10) by cross-multiplying to get y = 3*70/10 = 21. Similarly, we can determine x using the first ratio (x/y = 4/5) to find x = 4*21/5 = 16.8. For w, using the third ratio (z/w = 6/7), we have w = 70*7/6 = 81.666...
Now that we have the values of x, y, z, and w, we can substitute them into the expression xyw/z and get (16.8*21*81.666..)/70. Performing this calculation gives us the final answer, which completes our step-by-step solution to the original question.