Question

If Y varies inversely as twice x and when x = 3, y = 8 how do you find y when x = 2?

Answer 1

When `x=2, y = 12`

Explanation:

• Write the statement as an inverse proportion first:
  `y prop 1/(2x)`
• Change to an equation using a constant `k`

`y = k/(2x)," "` which can be written as `" "k = 2x xx y`

• Use the values given to find a value for `k`
  `k = (2xx3) xx8 = 48`

• Use the values for `k and x` to find `y`.

`y = k/(2x) = 48/(2xx2)`

`= 48/4 = 12`

Answer 2

y = 12

Explanation:

Here `y prop 1/(2x)`

or, `y = k. 1/(2x)` ..............(i)

put x = 3 & y = 8 we get, `8 = k. 1/(2xx3)`

`rArr k = 48`

Again putting the value of k & x in (i) to find 'y'

`rArr y = 48. 1/(2xx2)`

`rArr y = 12`