Finding the total using only the value and percentage?

Question

I've tried my best to google this, but I cannot seem to google it correctly or it's just not something people use that often.

I'm trying to essentially solve for X if the equation is:

80=80% of x

I'm just using 80 as an example as we indefinitely know that the answer is 100 in this scenario. How would one use just 80 and a percentage to get to the solution? Today was the first time I had to use this and would really like to know for future reference. Thank you!

Answer 1

Recall: if we have the statement $p\%$ of $x$, for whatever $p$ and $x$ are, the "of" means to multiply $p/100 \cdot x$.

Thus, $p=80$ in your scenario, and $80\%$ of $x$ becomes

$$\frac{80}{100} \cdot x =\frac 4 5 x$$

Thus we have

$$80 = \text{80% of x} \implies 80 = \frac 4 5 x$$

From here, just solve for $x$. (Hint: multiply both sides by $5/4$, the reciprocal of the coefficient of $x$.)

Answer 2

Let's consider $k \%$ of $x$

$k \% \ of \ x \ = \frac{k}{100}x $

So, $80 = \frac{k}{100}x$ or, $x = \frac{8000}{k}$

For different values of $k$, we get different $x$

$k = 10 \ , x = 800$

$k = 80 \ , x = 100$

$k = 100 \ , x = 80$ and so on