Question

X+y;y+z;z+x are in ratio 6:7:8 andx+y+z =14 the value of x

Answer 1

Answer:

Given:

x + y = 6n Equation 1

y + z = 7n Equation 2

z + x = 8n Equation 3

x + y + z = 14 Equation 4

Find:

x

Solutions:

We have four equations in 4 unknowns, so we may be able to solve.

Add Equations 1, 2, and 3

2x + 2y + 2z = 21n

x + y + z = (21/2)n

Substitute this value for x + y + z in Equation 4 and solve for n:

x + y + z = 14

(21/2)n = 14

21n = 28

n = 4/3

Solve Equation 1 for x:

x + y = 6n

x = 6(4/3) - y

x = 24/3 - y

Substitute this value of x into Equation 3:

z + x = 8n

z + 24/3 - y = 8(4/3)

z - y = 8/3

Add this to Equation 2 and solve for z:

y + z = 7n

z + y = 7(4/3)

z + y = 28/3

[z + y = 28/3] + [z - y = 8/3]

2z = 28/3 + 8/3

2z = 36/3

z = 18/3

Substitute into Equation 3 and solve for x:

z + x = 8n

18/3 + x = 8(4/3)

x = 14/3

Check:

Substitute x = 14/3 into equation 1 and solve for y:

x + y = 6n

14/3 + y = 6(4/3)

y = 10/3

Verify with equation 4:

x + y + z = 14

14/3 + 10/3 + 18/3 = 14

14 + 10 + 18 = 42

42 = 42 check