Question

15. The combined age of Archibald and
Bertie is 19. The com-bined age of
Archibald and Charlie is 37. The combined
age of Bertie and Charlie is 52. How old
is:Archibald?Bertie? Charlie?
Your answer​

Answer 1

Answer:

Let the age of Archibald be x years, Bertie be 19 y years, and Charlie be z years.

Given,

Combined age of Archibald and Bertie is 19

=> x + y = 19

=> x = 19 - y ... (1)

Combined age of Archibald and Charlie is 37

=> x + z = 37

=> 19 - y + z = 37   (from (1))

=> -y + z = 37 -19

=> -y + z = 18 .... (2)

Combined age of Bertie and Charlie is 52

=> y + z = 52.

=> z = 52 - y ... (3)

Substitue (3) in (2)

-y + 52 - y = 18

-2y + 52 = 18

-2y = 18 - 52

-2y = -34

y = -32/-2

y = 17

Substitute y = 17 in (3)

z = 52 - y

z = 52 - 17

z = 35

Substitue y = 17 in (1)

x = 19 - y

x = 19 - 17

x = 2

∴ The age of Archibald is 2 years, Bertie is 17 years, and Charlie is 35 years.