Question

What percent of 15,000 is 18,000?

Answer 1

`120%`

Explanation:

`x%" of "15000=18000`

`=>x/(1cancel(00))times150cancel(00)=18000`

`=>150x=18000`

Dividing both sides by 150,

`=>(cancel(150)x)/color(red)((cancel(150)))=18000/color(red)(150`

`=>x = 1800/15 = 120`

Therefore, `120%` of `15000` is `18000`.

Answer 2

Quick solution plus some teaching.

`120%`

Explanation:

Percentage is basically just a fraction. It is however a special fraction in that the denominator is always fixed at 100.

Thing is; there is a convention to use the symbol %.
This may be considered a `ul("bit"color(red)(" like"))` units of measurement but one that is worth `1/100`

This is similar ( just using 3 as it happened to come to mind)

`3 " centimetres"`

centi is `1/100color(white)()^("th")` so 3 cm `-> 3xx 1/100xx1" metre"`

`color(white)("dddddddddd")`Thus 3% `->3xx1/100xx"Something"`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(white)("dddddddddddd")color(blue)(ul(bar(|color(white)(2/2)"Quick solution "|)`

The wording 'percent of' make the 15000 the basis for comparison. So if we express this as a fraction we have:

`18000/15000`

`(18cancel(000))/(15cancel(000)`

`color(brown)("Shortcut method")`

`color(white)("d")18/15xx100` and stick a % on the end`->120%`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(brown)(" Why do we stick a % on the end?")`

Taking a step back we have: `18/15`

Fraction wise we need to change this to `color(white)("d")("something")/100`

Look at the denominator of 15 from `18/15`. If we do this to it `" "15xx100/15` we get 100. What we do to the bottom for multiply or divide we also do to the top.

Now look at the numerator of 18. We do this: `color(green)(" "18xx100/15)` that is the shortcut bit.

However, all of this is over the `color(blue)("final denominator of 100")`. So lets include this giving:

`color(green)(18xx100/15)color(blue)(xx1/100)`

but another way of writing `1/100` is % so we end up with `18/15xx100xx%`

But the same way in algebra we do not write (example) `3xx x` but `3x` then in the same way we do not write the cross for multiply in front of the %

THUS WE HAVE

`(18/15xx100)%-> 120%`

which is another way of saying `120xx1/100`