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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?

• $5$
• $20$
• $30$
• $25$
• $36$

algebra

Mean

Median

Check the Answer

But try the problem first…

Answer: $30$

Source
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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 $3(10)=30$