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

Try this beautiful problem from algebra, based on Sum of the numbers from AMC-10A, 2001. You may use sequential hints to solve the problem.

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

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 $3(10)=30$