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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

But try the problem first…

Answer: $7$

Source

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 $7$