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
In 2025, 8 students from Cheenta Academy cracked the prestigious Regional Math Olympiad. In this post, we will share some of their success stories and learning strategies. The Regional Mathematics Olympiad (RMO) and the Indian National Mathematics Olympiad (INMO) are two most important mathematics contests in India.These two contests are for the students who are […]
Cheenta Academy proudly celebrates the success of 27 current and former students who qualified for the Indian Olympiad Qualifier in Mathematics (IOQM) 2025, advancing to the next stage — RMO. This accomplishment highlights their perseverance and Cheenta’s ongoing mission to nurture mathematical excellence and research-oriented learning.
Cheenta students shine at the Purple Comet Math Meet 2025 organized by Titu Andreescu and Jonathan Kanewith top national and global ranks.
Celebrate the success of Cheenta students in the Stanford Math Tournament. The Unified Vectors team achieved Top 20 in the Team Round.