The average of the test scores of a class of p students is 70, and the average of the test scores of a class of n students is 92. When the scores of both classes are combined, the average score is 86. What is the value of p/n?
the total for the first class is 70p and the total for the second class is 92n
so the combined total is 70p+92n
but we are also told that the average score for both classes is 86
i.e. 86(p+n)
so 70p+92n = 86(p+n)
70p+92n=86p+86n
-16p=-6n
16p=6n
then p/n=6/16
p/n = 3/8
To solve for the value of p/n, let's start by simplifying the equation:
70p + 92n = 86(p + n)
Now, let's distribute the 86 on the right side of the equation:
70p + 92n = 86p + 86n
Next, let's group the variables (p on one side and n on the other) and the constant terms (70 and 86):
70p - 86p = 86n - 92n
Combine like terms:
-16p = -6n
To isolate p, divide both sides of the equation by -16:
p = (-6n) / (-16)
Simplify this fraction:
p = 3n / 8
Therefore, p/n can be expressed as 3/8.