50 is 125% of what number?

2 Answers
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 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 = 5/4 * x
10=1/4 * x (divide both sides by 5)
40 = x (multiply both sides by 4)

Jul 19, 2016

x=40

Explanation:

color(blue)("The explanation bit about the method")

Percentage can be presented in 2 ways.

Normally written in the form as 125%

For mathematical purposes as 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->2 apples-> 2xxapples

So 125% of unknown value is:

125/100xx x

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

125/100xx x =50

To get x on its own the trick is to turn 125/100 into 1

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

color(blue)("The calculation bit")

color(green)(125/100xx x= 50)
color(white)(.)

Multiply both side by color(red)(100/125)

color(green)(125/100color(red)(xx100/125)xx x=50color(red)( xx 100/125))

color(white)(.)

But 125/100xx100/125" " ->" " 125/125xx100/100" " =" " 1
color(white)(.)

x=50xx100/125

x= 50/125xx100

x=2/(cancel(5)^1)xxcancel(100)^(20)

x=40