Final answer:
To find the simplified integer ratio p:q:r, scale the first ratio p:q so that q matches the second ratio q:r. Combine them to get p:q:r = 35:55:9, which is already in the simplest form.
Step-by-step explanation:
To find the ratio p:q:r given that p:q equals 7:11 and q:r equals 55:9, we first need to make the 'q' in both ratios correspond to the same number. We can do this by finding a common multiple of the two 'q' values in the given ratios, which are 11 and 55. The smallest common multiple of 11 and 55 is 55. We can now scale up the first ratio by multiplying both terms of the ratio p:q = 7:11 by 5, which gives us p:q = 35:55. The second ratio, q:r, is already in the form of 55:9, so we do not need to change it.
Now we can combine these to find the compound ratio of p to q to r. Since q is the same in both (55), the compound ratio is simply the ratios put together, which yields p:q:r = 35:55:9.
Finally, we simplify this integer ratio to its simplest form by finding the greatest common divisor of the three numbers and dividing each part of the ratio by that number. The greatest common divisor of 35, 55, and 9 is 1, so the ratio is already in its simplest form. Thus, the simplest form of the ratio is 35:55:9.