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. 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

Answer:

4/3 , 5 , 26/3

Step-by-step explanation:

x+ y + z = 15. .......(i)

according to first condition given in question

(x+z) - y = 5. ........( ii)

and according to the second condition

2(x+y) - z = 4. ..........( iii)

now from eqn.(i), x + z = 15 - y. .......( iv)

putting this value in eqn.(ii),we get

(15 - y )- y = 5

15 - 2 y = 5

-2 y = 5 - 15

-2y = -10

y = 5

from eqn. ( iv) ., x + z = 15-5= 10.

x = 10- z ....( v)

from (iii)

2 x + 2 y - z = 4

2(10-z) + 2 × 5 - z =4

20 - 2z + 10 -z = 4

30 - 3z = 4

-3z = 4-30

-3z = -26

z = 26/3

putting value of y and z in eqn. (i)

x+ 5+ 26/3 = 15

x = 15 - 5 - 26/3

x= 10 -26/3 = (30-26)/3 = 4/3

Hence,the three numbers are 4/3, 5, 26/3