Carcass wrote:
The ratio of p to q to r is 2:7:11, and r is 6 greater than the sum of p and q. What is the value of p + r ?
(A) 27
(B) 33
(C) 39
(D) 54
(E) 60
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