37.5 is 60% of what number?

2 Answers
Nov 16, 2016

Answer:

37.5 is 60% of 62.5#

Explanation:

First, let's call the number we are looking for #n#.

"Percent" or "%" means "out of 100" or "per 100", Therefore 60% can be written as #60/100#.

When dealing with percents the word "of" means "times" or "to multiply".

So, putting this all together allows us to write the following equation and solve for #n# while keeping the equation balanced:

#60/100 xx n = 37.5#

#100/60 xx 60/100 xx n = 100/60 xx 37.5#

#1 xx n = 3750/60#

#n = 62.5#

Nov 16, 2016

Answer:

The number is 62.5

Explanation:

#color(blue)("The general principle")#

% is units of measurement and % is worth #1/100#

So #60% -> 60xx1/100 = 60/100#

Using the principle of ratios, which really is the same thing as
smendyker used. It just looks different.

Consider #60/100# as the reference ratio giving us:

#60/100-=37.5/("some unknown value")#

Let the unknown value be #x# giving:

#60/100-=37.5/x#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Building the conversion method")#

These are ratios and equivalent to each other ( #-=#)

Then if I maintain the ratio but change the 60 into 37.5 I will find out what #x# is worth.

Step 1: change 60 into 1# ->60 -:60 = 60xx1/60 = 1#

Step 2: multiply the 1 by 37.5#-> 60xx1/60xx37.5 = 60xx37.5/60#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Applying the conversion method")#

Multiply by 1 but in the form of #1=(color(white)(.)37.5/60color(white)(.))/(37.5/60)#

#color(green)([60/100color(magenta)(xx1)]->[60/100color(magenta)(xx(color(white)(.)37.5/60color(white)(.))/(37.5/60) ) ]#

#=37.5/62.5#

So the number is 62.5
...................................................................
That is: #60/100xx62.5 = 37.5#