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


But try the problem first…

Answer: \(30\)

Source
Suggested Reading

AMC-10A (2001) Problem 16

Pre College Mathematics

Try with Hints


First hint

 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 ……….

Second Hint

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

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

\(\Rightarrow m=10\)

Final Step

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

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