Question

112 is 76% of what?

Answer 1

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`