Question

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

Answer 1

Answer:

$\frac{3}{8}$

Step-by-step 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):

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