Question

The variable z is directly proportional to x, and inversely proportional to y. When x is 8 and y is 18, z has the value 1.3333333333333. What is the value of z when x= 13, and y= 22

Answer 1

The variable z is directly proportional to x, and inversely proportional to y,where k is the constant of proportionality. When, x=8 and y=18, z is 1.33.

So, plugging x,y and z in z=k\frac{x}{y} to get the value of k we get, To isolate, k let us multiply by 18 on both sides

1.33*18=k

23.99=k

So, 23.99=8k

To solve for k, let us divide by 8 on both sides. Let us plug k=3, x=13 and y=22 to solve for z.

z=1.77

Answer: z=1.77

Answer 2

The variable z is directly proportional to x, and inversely proportional to y.

`z\alpha x`

and

`z\alpha (1)/(y)`

So,
`z\alpha (x)/(y)`

`z=k(x)/(y)`

where, k is the constant of proportionality.

When, x=8 and y=18, z is 1.33.

So, plugging x,y and z in z=k\frac{x}{y} to get the value of k we get,

`1.33=k(8)/(18)`

To isolate, k let us multiply by 18 on both sides

1.33*18=k
`(8*18)/(18)`

23.99=k
`(8*1)/(1)`

So, 23.99=8k

To solve for k, let us divide by 8 on both sides

`(23.99)/(8)=(8)/(8) k`

2.99=
`(1k)/(1)`

k=3

Let us plug k=3, x=13 and y=22 to solve for z

`z=3*(13)/(22)`

z=
`(39)/(22)`

z=1.77

Answer: z=1.77