Question

If y varies inversely as x, and y = 6 when x = 24, find x when y = 18

Answer 1

x = 8

Explanation:

Standard form for inverse variation:

y = k/x

We now use the given information to find k.

y = 6 when x = 24

6 = k/24

k = 6 * 24

k = 144

The equation for this inverse relation is

y = 144/x

For y = 18, we get

18 = 144/x

18x = 144

x = 144/18

x = 8

Answer 2

x = 8

Explanation:

To find the value of x when y = 18 we must first find the relationship between them.

The statement

y varies inversely as x is written as

`y \: \: \alpha \: \: (k)/(x)`

where k is the constant of proportionality

From the question when

y = 6

x = 24

Substitute the values into the above equation

That's

`6 = (k)/(24)`

Cross multiply

That's

k = 24(6)

k = 144

So the formula for the variation is

`y = (144)/(x)`

When

y = 18

`18 = (144)/(x)`

Cross multiply

18x = 144

Divide both sides by 18

x = 8

Hope this helps you