Question

Q.2) The sum of three numbers is 15. If the
second number is subtracted from the sum
of first and third numbers then we get 5.
When the third number is subtracted from
the sum of twice the first number and the
second number, we get 4. Find the three
numbers.
​

Answer 1

Given data :

• The sum of three numbers is 15.

• If the second number is subtracted from the sum of first and third numbers then we get 5.

• When the third number is subtracted from the sum of twice the first number and the second number, we get 4.

To find : The three numbers ?

Solution : Let, the three numbers be x, y and z.

Let,

• First number be x
• Second number be y
• Third number be z

Now, according to given,

→ x + y + z = 15 ........( 1 )

From eq. ( 1 ) we need to make two equation,

→ x + z = 15 - y ......( 2 )

→ x + y = 15 - z .......( 3 )

Now, according to given,

→ ( x + z ) - y = 5 .......( 4 )

→ 2 * ( x + y ) - z = 4 .......( 5 )

Now, put value of ‘ x + z ’ from eq. ( 2 ) into eq. ( 4 ), hence eq. ( 4 ) become's,

→ ( x + z ) - y = 5

→ 15 - y - y = 5

→ 15 - 2y

→ - 2y = 5 - 15

→ - 2y = - 10

{ minus ( - ) sign cancel from both side }

→ 2y = 10

→ y = 10/2

→ y = 5 .......( 6 )

Now, put value of ‘ x + y ’ from eq. ( 3 ) into eq. ( 5 ), hence eq. ( 5 ) become's,

→ 2 * ( 15 - z ) - z = 4

→ 30 - 2z - z = 4

→ 30 - 3z = 4

→ - 3z = 4 - 30

→ - 3z = - 26

{ minus ( - ) sign cancel from both side }

→ 3z = 26

→ z = 26/3 ........( 7 )

Now, put value of y and z from eq. ( 6 ) and eq. ( 7 ) respectively, into eq. ( 1 )

→ x + y + z = 15

→ x + 5 + 26/3 = 15

→ x + 15/3 + 26/3 = 15

→ x + {15 + 26}/3 = 15

→ x + 41/3 = 15

→ x = 15 - 41/3

→ x = 45/3 - 41/3

→ x = {45 - 41}/3

→ x = 4/3 .......( 8 )

Answer : Hence, from eq. ( 6 ) eq. ( 7 ) and eq. ( 8 ) the value of three numbers x, y and z is 4/3, 5, and 26/3 respectively.

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Answer 2

Correct question :

The sum of three numbers is 15. If the

second number is subtracted from the sum of first and third numbers then we get 5. If twice of first number is added to the second number and if the third number is subtracted from the sum, we get 4. Find the three numbers.

Solution :

Given :

• The sum of three numbers = 15

• If the second number is subtracted from the sum of first and third numbers then we get 5.

• If twice of first number is added to the second number and if the third number is subtracted from the sum, we get 4.

According to the question :

Let the three numbers be ' x ', ' y ' and ' z '

• x + y + z = 15 ...... (1)

The second number is subtracted from the sum of first and third numbers then we get 5.

• x - y + z = 5 ...... (2)

Twice of first number is added to the second number and if the third number is subtracted from the sum, we get 4.

• 2x + y - z = 4 ...... (3)

Subtracting (1) - (2),

⟹ x + y + z = 15

⟹ x - y + z = 5

cancel ( ' x ' & ' x ' ) & ( ' z ' & ' z ' )

⟹ 2y = 10

⟹ y = 10 / 2

⟹ y = 5

Substituting ' y = 5 ' in (1),

⟹ x + y + z = 15

⟹ x + 5 + z = 15

⟹ x + z = 15 - 5

⟹ x + z = 10

⟹ z = 10 - x ...... (4)

Substituting ' z = 10 - x ' in (3),

⟹ 2x + y - z = 4

⟹ 2x + ( 10 - x ) - z = 4

⟹ 2x + x - ( 10 - 5 ) = 4

⟹ 3x - 5 = 4

⟹ 3x = 4 + 5

⟹ 3x = 9

⟹ x = 9 / 3

⟹ x = 3

Substituting ' x = 3 ' in (4),

⟹ z = 10 - x

⟹ z = 10 - 3

⟹ z = 7

∴ x = 3, y = 5 & z = 7

So It's Done !!