How Cheenta works to ensure student success?
Explore the Back-Story

# Sum of whole numbers | AMC-10A, 2012 | Problem 8

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?

• $8$
• $9$
• $7$
• $6$
• $5$

Algebra

Equation

Sum of digits

## Check the Answer

Answer: $7$

AMC-10A (2012) Problem 8

Pre College Mathematics

## Try with Hints

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 $7$

## Subscribe to Cheenta at Youtube

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?

• $8$
• $9$
• $7$
• $6$
• $5$

Algebra

Equation

Sum of digits

## Check the Answer

Answer: $7$

AMC-10A (2012) Problem 8

Pre College Mathematics

## Try with Hints

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 $7$

## Subscribe to Cheenta at Youtube

This site uses Akismet to reduce spam. Learn how your comment data is processed.

### Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy

### Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.
HALL OF FAMEBLOG
CHEENTA ON DEMANDBOSE OLYMPIAD
CAREERTEAM
support@cheenta.com