if x varies directly as the sum of reciprocals of y and z, and x=7 when y=2 and z=5. find the value of y when x=20 and z=2.

Question

if x varies directly as the sum of reciprocals of y and z, and x=7 when y=2 and z=5. find the value of y when x=20 and z=2.

Answer 1

x = k(1/y + 1/z)

 

7 = k(1/2 + 1/5)

 

7 = (7/10)k

 

So, k = 10

 

x = 10(1/y + 1/z)

 

If x = 20 and z = 2, we have 20 = 10(1/y + 1/2)

 

1/y + 1/2 = 2

 

1/y = 3/2

 

y = 2/3