The ratio of p to q to r is 2:7:11, and r is 6 greater than the sum of

Nice question!

Let's rewrite all three values (\(p\), \(q\) and \(r\)) in terms of ONE variable.

To begin, we can see that \(\frac{p}{q} = \frac{2}{7}\)
Cross multiply to get: \(2q = 7p\)
Divide both sides by \(2\) to get: \(q = \frac{7p}{2}\)


Similarly, we can see that \(\frac{p}{r} = \frac{2}{11}\)
Cross multiply to get: \(2r = 11p\)
Divide both sides by \(2\) to get: \(r = \frac{11p}{2}\)

r is 6 greater than the sum of p and q.
In other words: \(r - (p + q) = 6\)
Substitute values to get: \(\frac{11p}{2} - (p + \frac{7p}{2}) = 6\)
To eliminate the fractions, multiply both sides by 2 to get: \(11p - (2p + 7p) = 12\)
Simplify: \(2p = 12\), which means \(p = 6\)

What is the value of \(p + r\) ?
Now that we know \(p = 6\), we can calculate the value of \(r\) as follows: \(r = \frac{11p}{2}= \frac{11(6)}{2}=33\)
\(p + r = 6 + 33 = 39\)

Answer: C