Question

The sum of three numbers is 10 . If the third number is equal to the sum of the first two numbers, while second number is 2 less than the sum of first and third, find numbers

Answer 1

Answer:

x = 1, y = 0, z = 1

Step-by-step explanation:

Let the numbers be x, y, z

z = x + y

y = (x + z) - 2                                  ..............(1)

==> z = x + y

==> y = z - x                                   ..............(2)

Putting value of eq(2) in eq(1), we get,

==> z - x = x + z - 2

==> z - z - x - x = - 2

==> -2x = - 2

∴ x = 1                                            ...................(3)

Putting value of eq(3) in eq(1) and eq(2), we get,

y =  (x + 1) - 2       ==>   y = x -1                                 .........................(4)

Also y = z - 1                                      .........................(5)

Equating eq(4) and eq(5),

x - 1 = z - 1

∴ x  = z = 1                           .......................(6)

Putting value of eq(6) in eq(4),

y = x - 1    ==>   y = 1-1   ==> y = 0