u : v = 4 : 7 and v : w = 9 : 7. If u = 72, then what is the value of w?

Step 1: From the first ratio, we know that u : v = 4 : 7. Given that u = 72, we can set up the equation 4/7 = 72/v to solve for v.

Step 2: Cross-multiplying gives us 4v = 504.

Step 3: Solving for v, we get v = 504 / 4 = 126.

Step 4: Now, we know that v : w = 9 : 7. We can set up the equation 9/7 = 126/w to solve for w.

Step 5: Cross-multiplying gives us 9w = 882.

Step 6: Solving for w, we get w = 882 / 9 = 98.

So, the value of w is 98.