The arithmetic mean is the simplest and most widely used measure of a mean, or average. It simply involves taking the sum of a group of numbers, then dividing that sum by the count of the numbers used in the series.
The numbers 3,5,7,a and b have an average of 15. What is the average of a and b ?
American Mathematics Competition 10 (AMC 10), {2020}, {2}
Average
3 out of 10
A Study of Experts understanding of Arithmetic Mean
Here is the first hint for this sum:
Try to find the arithmetic mean of the given numbers
i.e : \(\frac {3+5+7+a+b}{5}\)
=\(\frac {15+a+b}{5}\)
Now the arithmetic mean that we found in hint is actually equal to 15 given in the problem..
so \(\frac {15+a+b}{5} = 15\)
\(a+b = 60 \)
So final step will be : if we divide the expression of hint 2 we can find the average of a and b
Answer : \(\frac {60}{2} = 30 \)
AMC - AIME Boot Camp... for brilliant students.
Use our exclusive one-on-one plus group class system to prepare for Math Olympiad
