Question

One day, 32 of 80 people wore a red shirt to school. What percent of the 80 people did not wear a red shirt to school?

Answer 1

60 percent

Explanation:

Let me start with finding number of people who wore other colored shirt:

`=80-32 = 48`

Therefore, 48 out of 80 people wore other colored shirt.

As percentage this is:

`=100times48/80 = 60` percent

Your answer is 60%.

Answer 2

`60%`

A lot of detail given to help understanding. Normally a calculation of this type would only take a few lines.

Explanation:

Percentage is basically just another fraction. Although, it is a special fraction in that the bottom number (denominator) is fixed at 100.

If the count of red shirts is 32 then the non red shirt count is
`80-32 = 48`

So this count as a fraction of the whole is `48/80`

But for this to be a percentage we need the bottom number (denominator) to be 100. So we write as an 'equivalent fraction'.

Let the unknown count be `x` giving:

`color(green)(48/80-=x/100)`

To find the value of the top number (numerator) of `x` we need to get it on its own. So we need to 'get rid' of the 100. We do this by changing it into 1

Multiply both sides by color(red)(100)

`color(green)(48/80-=x/100 color(white)("dddd")->color(white)("dddd") 48/80color(red)(xx100) color(white)("d") =color(white)("d") x/100color(red)(xx100) )`

`color(green)(color(white)("ddddddddddd.d") ->color(white)("dddd") 48color(red)(xxcancel(100)^(10)/color(green)(cancel(80)^8)) color(white)("d") =color(white)("d") xcolor(red)(xxcancel(100)/color(green)(cancel(100))) )`

`color(green)(color(white)("ddddddddddd.d") ->color(white)("ddddddd") cancel(48)^6xx10/cancel(8)^1 color(white)("d") =color(white)("d") x)`

`color(green)(color(white)("ddddddddddd.d") ->color(white)("ddddddddddd") 60color(white)("dddd") =color(white)("d") x)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`x=60 ->x/100=60/100`

`60/100` is the same thing as `60xx1/100` and `xx1/100` is the same thing as `%`

So `60/100=60%`