helping solving for y and x

Question

 

 

1.  if y varies directly with x and y = 10 when x - 15, find y when x = 6

 

2.  if x varies inversely as y and x = 2 when y = 8, find x when y = 17

 

3.  if y varies directly as x and inversely as z^2, and y = 3 when x = 2 and z = 4, what is the value of x when y = 6 and z = 2

 

thanks

Answer 1

1.y=ax ( varies directly) y=10 when x=15 so a=10/15 or 2/3, so y=(2/3)x when x=6 y=(2/3)*6=4

    

2.x=a/y( varies inversely), x=2,y=8 a=16, so x=16/y,  when y=17 x=16/17

 

3. y=ax/(z²), y=3 when x=2 and z=4, 3=2a/16 or a=24 so y=24x/(z²), x=?when y=6 and z=2, x=y*(z²)/24

    so x=1

 

Jim