Question

The sum of ages of A and B is 72years,B and C is 65years,A and C is 41 years then the sum of A,B and C is____​

Answer 1

Answer:

The sum of the ages of A, B and C is 89 years.

Step-by-step explanation:

Given :

• The sum of ages of A and B is 72 years
• The sum of ages of B and C is 65 years
• The sum of ages of A and C is 41 years

To find :

The sum of ages of A,B and C

Solution :

Let

• the age of A be x years
• the age of B be y years
• the age of C be z years

⇾ The sum of ages of A and B is 72 years.

x + y = 72 ➙ (1)

⇾ The sum of ages of B and C is 65 years.

y + z = 65 ➙ (2)

⇾ The sum of ages of A and C is 41 years.

x + z = 41 ➙ (3)

Subtract equation (2) from equation (1);

x + y - (y + z) = 72 - 65

x + y - y - z = 7

 x - z = 7 ➙ (4)

Add equations (3) and (4);

x + z + x - z = 41 + 7

  2x = 48

   x = 48/2

   x = 24 years

∴ The age of A is 24 years.

Substitute x = 24 in equation (1);

  x + y = 72

 24 + y = 72

  y = 72 - 24

  y = 48 years

∴ The age of B is 48 years.

Substitute x = 24 in equation (3);

x + z = 41

24 + z = 41

z = 41 - 24

z = 17 years

∴ The age of C is 17 years

➣ The sum of the ages of A, B and C

    = x + y + z

    = 24 years + 48 years + 17 years

    = 89 years

Answer 2

Step-by-step explanation:

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given,

1)sum of ages of A and B = 72years

= A+B = 72years

2) sum of ages of B and C = 65years

= B+C = 65years

3) sum of ages of A and C = 41years

= A+C = 41 years

.: adding all equations

= A+B+B+C+A+C = 72years+65years+41years

= 2A+2B+2C = 178years

= 2(A+B+C) = 178years

= A+B+C = 178/2 = 89

.: sum of ages of A,B,C = 89years