Try this beautiful problem from Algebra based on Sum of the numbers….

## Sum of the numbers – AMC-10A, 2001- Problem 16

The mean of three numbers is $10$ more than the least of the numbers and $15$ less than the greatest. The median of the three numbers is $5$. What is their sum?

- \(5\)
- \(20\)
- \(30\)
- \(25\)
- \(36\)

**Key Concepts**

algebra

Mean

Median

## Check the Answer

Answer: \(30\)

AMC-10A (2001) Problem 16

Pre College Mathematics

## Try with Hints

Mean of three numbers means average of three numbers……

Let \(x\) be the mean of three numbers then we can say that the least of the numbers is $m-10$ and the greatest is $m + 15$

Can you now finish the problem ……….

Given that The median of the three numbers is $5$. Now “median” means the middle of the three numbers

so we can write $\frac{1}{3}[(m-10) + 5 + (m + 15)] = m$,

\(\Rightarrow m=10\)

Therefore The sum of three numbers are \(3(10)=30\)

## Other useful links

- https://www.cheenta.com/sum-of-the-digits-amc-10a-2007-problem-25/
- https://www.youtube.com/watch?v=fRj9NuPGrLU