What is the value of x in the equation .4 = [20%]/[x]?

[Tarnix]

Homework Statement

.4 = [20%]/[x]

Homework Equations

The Attempt at a Solution

This is what I tried...but I know this isn't right as I need an actual value for x.

.4 = (.2)(x^-1)
.4 / .2 = x^-1
2 = x^-1
2 = 1 / x

 

[AngusYoung93]

You're almost done. multiply both sides by x, then divide by 2.

 

[Tarnix]

2(x) = (1/x)(x)
2x = 1
x = 1/2

Is that right?

 

[AngusYoung93]

aye.

 

[rocomath]

$$.4=\frac{.2}{x}$$

Converting decimals to fractions ...

$$.4=\frac{4}{10}=\frac 2 5$$

$$.2=\frac{2}{10}=\frac 1 5$$

Substituting ...

$$\frac 2 5 = \frac{1}{5x}$$

 

[Tarnix]

I don't think that is correct. If I solved Roco's equation I would get:
2/5 = 1/5x
(2/5) / (1/5) = x
2 = x

When really the solution is .5

I think you mean by substituting fractions would be...
2/5 = (1/5) / x

But thank you for trying to help :D I just don't want someone else to get confused if they look at this later.

 

[cristo]

I don't think that is correct. If I solved Roco's equation I would get:
2/5 = 1/5x
(2/5) / (1/5) = x

No you wouldn't, you'd get $$\frac{2/5}{1/5}=\frac{1}{x} \Rightarrow x=\frac{1}{2}$$