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
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\(p : q : r = 2x : 7x : 11x\)

\(p + q = 9x\) & \(r = 11x\)

So, \(11x - 9x = 6\)

Thus, \(x = 3\)

Hence, \(p + r = 3(2 + 11) =39\), Answer msut be (C)
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Nice question. I spent way too much time on this at first.

We are given all items in relation to each other, which can be translated as; p/2=q/7=r/11.
Furthermore, we are given r=p+q+6.

And finally, we need to find r+p =?.

Step 1) Calculate what r is in terms of p
r=11p/2

Step 2) insert in question
r+p = 11p/2+p = 13p/2

So we want to know the value of p now.

Step 3) Calculate the value of p by substituting everything into the other equation based on the ratios:
r=p+q+6 =>
11p/2 = p + (7p/2) +6
11p/2 = 9p/2 + 6
2p/2 = 6
p = 6

Step 4) is filling in p in the question (as calculated in step 1)

13p/2 = (13*6)/2 = 13*3 = 39

p = 39 is answer C

r = (p + q) + 6
11x = (2x + 7x) + 6
11x - 9x = 6
X = 3

P = 2x = 2*3 = 6
R = 11x = 11*3 = 33
P+ R = 33+6 = 39
Option C = 39

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If p = 2 , q = 7 and r = 11 then r(11) is 2 greater than (p + q = 2 + 7 = 9)

For 'r' to be '6' greater, multiply the values by '3'.

p = 6, q = 21 and r = 33 => 33 is '6' greater than (p + q = 6 + 21 = 27)

Hence, p + r = 6 + 33 = 39

Answer C
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