50 is 125% of what number?

Jul 19, 2016

40

Explanation:

I like to solve these problems by translating it into math. The key words in this question are is and of. Is can be translated to $=$ and of can be translated into multiplication. With these kinds of problems it's good to say "of means multiply". Now what number can be translated into a variable, I'll just use $x$.

Now we'll need to turn 125% into a number we can work with. We can use $1.25$ (divide the percentage by $100$) then turn $1.25$ into $\frac{5}{4}$ which will work nicely with the arithmetic for this problem.

So using that let's try to turn this into a problem we can solve for.

$50 = \frac{5}{4} \cdot x$
$10 = \frac{1}{4} \cdot x$ (divide both sides by 5)
$40 = x$ (multiply both sides by 4)

Jul 19, 2016

$x = 40$

Explanation:

$\textcolor{b l u e}{\text{The explanation bit about the method}}$

Percentage can be presented in 2 ways.

Normally written in the form as 125%

For mathematical purposes as $\frac{125}{100}$

Let the unknown value be $x$

The word in the question "of" really means multiply.
This is a bit like 2 of apples$\to$2 apples$\to 2 \times$apples

So 125% of unknown value is:

$\frac{125}{100} \times x$

We are told that the answer to this is 50 so we have

$\frac{125}{100} \times x = 50$

To get $x$ on its own the trick is to turn $\frac{125}{100}$ into 1

What you do to 1 side of an equation you do to the other side.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$\textcolor{b l u e}{\text{The calculation bit}}$

$\textcolor{g r e e n}{\frac{125}{100} \times x = 50}$
$\textcolor{w h i t e}{.}$

Multiply both side by $\textcolor{red}{\frac{100}{125}}$

$\textcolor{g r e e n}{\frac{125}{100} \textcolor{red}{\times \frac{100}{125}} \times x = 50 \textcolor{red}{\times \frac{100}{125}}}$

$\textcolor{w h i t e}{.}$

But $\frac{125}{100} \times \frac{100}{125} \text{ " ->" " 125/125xx100/100" " =" } 1$
$\textcolor{w h i t e}{.}$

$x = 50 \times \frac{100}{125}$

$x = \frac{50}{125} \times 100$

$x = \frac{2}{{\cancel{5}}^{1}} \times {\cancel{100}}^{20}$

$x = 40$