112 is 76% of what?

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Answer 1 · 2016-11-30T17:57:28

The answer is #2800/19=147,368421...#

Here's how I did it :

Let's consider that 112 is 76% of something that we'll name x.

This x represents the Whole which is in percentage 100% and 112 is a portion of it which is in percentage 76%

#112 -> 76%#
#x -> 100%#

Theses numbers are connected in a way that :

#x/112=(100cancel%)/(76cancel%) -> x/112= 100/76#

Same thing as : #112/x=(76cancel%)/(100cancel%) -> 112/x=76/100#

To find #x# we need the solve one of the equations above, let's say the 2nd :

#(112xxcolor(red)100)/(x xxcolor(red)100)=(76xx color(blue)x)/(100xx color(blue)x)#

Since we have the SAME denominator #(100xx x)# then the numerators must be equal.

#112xxcolor(red)100=76xx color(blue)x#

#(112xxcolor(red)100)/76=color(blue)x#

Simplify that :

#x=112/76 xx100 = (56xxcancel2)/(38xxcancel2) xx100 = (28xxcancel2)/(19xxcancel2) xx100#

19 is a prime number and is not a divisor of 2800 so:

#x=2800/19=147,368421...#

So 112 is 76% of #2800/19#