Try this beautiful problem from Algebra based on Sum of whole numbers.
Sum of whole numbers – AMC-10A, 2012- Problem 8
The sums of three whole numbers taken in pairs are 12, 17, and 19. What is the middle number?
- \(8\)
- \(9\)
- \(7\)
- \(6\)
- \(5\)
Key Concepts
Algebra
Equation
Sum of digits
Check the Answer
But try the problem first…
Answer: \(7\)
AMC-10A (2012) Problem 8
Pre College Mathematics
Try with Hints
First hint
Let us assume three numbers are \(x\),\(y\) and \(z\)
Now according to the problem
\(x+y=12\)…………………(1)
\(y+z=17\)………………..(2)
\(z+x=19\)………………….(3).
Can you find out the values of \(x\),\(y\) and \(z\)…………….?
can you finish the problem……..
Second Hint
Adding three equations we get \(2(x=y+z)=48\)
\(\Rightarrow x+y+z=24\)………….(3)
Now subtract (3) from (1),we will get \(z=12\) and similarly if we subtract (2) and (3) from (1) we will get \(x=7\) and \(y=5\)
can you finish the problem……..
Final Step
Therefore,the numbers are \(12\), \(7\), and \(5\) and middle number is \(7\)
Other useful links
- https://www.cheenta.com/cubical-box-amc-10a-2010-problem-20/
- https://www.youtube.com/watch?v=uApjRLII6YI
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