Question

In a class of p students, the average (arithmetic mean) of the test scores is 70.

In another class of n students, the average of the scores for the same test is 92.
When the scores of the two classes are combined, the average of the test scores is 86.

What is the value of p/n?"

Answer 1

`(3)/(8)`

Explanation:

The average of a set of
`n` values is equal to the sum of all values in that set divided by
`n`.

Conceptually, if
`p=n`, the average should the mean of 70 and 92, which is 81. Since the combined mean is actually 86, we know that
`n>p` (just something to keep in the back of your mind).

To solve, write an equation using the definition of arithmetic mean (refer to the first sentence in the answer):

`(70p+92n)/(p+n)=86,\\70p+92n=86(p+n),\\70p+92n=86p+86n,\\6n=16p,\\(p)/(n)=(6)/(16)=\boxed{(3)/(8)}`