112 is 76% of what?

1 Answer
Nov 30, 2016

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

Explanation:

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