Question

If y varies directly with x and y= 12 when x= 16, what is the value of x when y= 5?

Answer 1

`x = 6 (2)/(3)`

Explanation:

Since y varies directly with x,

y= kx, where k is a constant.

① Find the value of the constant k.

When y=12, x= 16,

12= k(16)

16k= 12

`k = (12)/(16) \\ k = (3)/(4)`

②Substitute the value of k back into the equation:

`y = (3)/(4) x`

③ Find value of x when y=5.

When y=5,

`5 = (3)/(4) x \\ x = 5 / (3)/(4) \\ x = 5 * (4)/(3) \\ x = (20)/(3) \\ x = 6 (2)/(3)`