Question

4.If x+y, yuz, z+x are in the ratio 6:7:8 and x + y + z =14 then the value of x is(a) 6(b) 7(c) 8(d) 10​

Answer 1

Answer:

x = 14/3, y = 10/3, z = 6

Step-by-step explanation:

(x + y)/ (y + z) = 6/7

7x + 7y = 6y + 6z

So, 7x + y - 6z = 0 ---- (1)

(y + z)/ (z + x) = 7/8

8y + 8z = 7z + 7x

8y + z - 7x = 0  ---- (2)

(x + y)/ (z + x) = 6/8

8x + 8y = 6z + 6x

2x + 8y - 6z = 0 ---- (3)

From (1) and (3) we get since 6z is common in both,

x = 7/5 y --- (4)

Putting (1) we get,

z = 9y/5 --- (5)

Now, x + y + z = 14

Solving from (4) and (5) we get,

y = 10/3

Putting in (4) we get,

x = 14/3

z = 14 - 10/3 - 14/3

z = 6

So, x = 14/3, y = 10/3, z = 6