Test 8 Section 3 - #18 (page 835)

Now, normally we'd love to use Plug-In on a question like this, what with the variables and all.  Unfortunately, because the question is asking us, in the end, for p/n, we can't exactly just make up p and n, you know?  This one is supposed to be hard, and it is.  That's why this is a #18!  Anyway, to solve, we're going to have to use the Average Table (yay!), with variables in it (yuck!).  Here goes:

[# of Numbers]	[Average]	[Sum]
p	70	70p
n	92	92n
p + n	86	70p + 92n

Remember, the Average Table is based on the fact that [# of Numbers] x [Average] = [Sum].  We can add and/or subtract up and down the outer columns, but we can only fill in the middle column based on what we know from the question, or what we can figure out from the outer columns.

We get the sums (with variables) to be 70p, and 92n.  We know that the total number of kids (both classes) is going to be p + n.  We know that their average is going to be 86.  And filling in from the chart, we know the sum that gets us there is 70p + 92n.

That's as far as we can get w/ the average table, but it's far enough.  Here's what I've got written down at this point:

(p + n) * 86 = (70p + 92n)

Remember, [# of Numbers] x [Average] = [Sum]

Then, we just do some algebra.  Distribute:

86p + 86n = 70p + 92n

combine the p's and n's:

6n = 16p

and...go for the gold.  They want p/n.  Let's give it to them.

p/n = 6/16

that simplifies to

p/n = 3/8, which is the answer.  Phew.