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?

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........

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........

Therefore,the numbers are \(12\), \(7\), and \(5\) and middle number is \(7\)

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