Question

If three numbers are added the sum is $15$. If the second number is subtracted from the sum of first and third number then we get $5$. If twice the first number is added to the second and third number is subtracted from the sum we get $4$.Find the three numbers.

Answer 1

Let a,b,c be the three numbers

Given a+b+c = 15 _________ (1)

(a+c) - b = 5 _________ (2)

(2a + b) - c = 4 _________ (3)

a+b+c=15 _____ (1)

a-b+c= 5 ______ (2)

2a+b-c = 4 _______ (3)

(1)+(2) $\Rightarrow$ a+b+c+a-b+c = 15+5

2a+2c=20 (or) a+c= 10 ________ (4)

substituting (4) in (1) $\Rightarrow$ b+(a+c) = 15

$\Rightarrow$ b+10=15

$\Rightarrow$ b= 15 - 10 = 5

equation (1) + equation (3)

$\Rightarrow$ a+b+c+2a+b-x= 15+4

$\Rightarrow$ 3a+2b=19 $\Rightarrow$ 3a =19-2b

$\Rightarrow$ 3a=19-2(5)

$\Rightarrow$ 3a=19-10 = 9

$\therefore a=9/3=3$

$\therefore$ a = 3 , b = 5

put a = 3, b = 5 in (1) we get

3+5+c = 15

$\Rightarrow$ c = 15 - 8 = 7

$\therefore$ a = 3 b = 5 c = 7.