50 is 125% of what number?

2 Answers
Jul 19, 2016

Answer:

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

Answer:

#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#-> 2xx#apples

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#