Question

Question #aa7f0

Answer 1

Your tip would be `$7.60` so your total would be:

`38+3.80 = $45.60.`

Explanation:

With simple percentages like `10%, 20%` I move the decimal point over one to the left .

(`10% " of " $38.00 rarr $3.80` and `20% rarr 2xx3.80`).

After doing that I multiply giving me `$7.60`.

Answer 2

`$45.60`

Explanation:

`color(blue)("The teaching bit")`

Percentage is just a fraction but a special one. What make it special is that the bottom number (denominator) is fixed at 100.

As an example `30% ->30/100` this is stating that if there are 100 of something you have selected 30 of them.

Now let look at the symbol %. In a way this is a bit like the
c in cm`->` centimetres ( centi metres)

Note that centi is another way of saying
`100color(white)()^("th")->1/100" of 1 metre"`

As cm is a unit of measurement then so is `%` a unit of measurement but one that represents `1/100`

So 20% `->20xx%color(white)("d")->color(white)("d")20xx1/100=20/100`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answering the question")`

`color(brown)("The tip part")`

`color(white)("d")20% color(white)("d")"of "color(white)("dd")$38`
`color(white)("d")color(red)(darr)color(white)("ddd")color(red)(darr)color(white)("ddd")color(red)(darr)`
`20/100color(white)("dvd")xxcolor(white)("dd")$38`

But `20/100` is the same as `(20-:20)/(100-:20)=1/5` so now we have:

`1/5xx$38.00=$7.60`

So `20%" of "$38=$7.60`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(brown)("Putting all of this together")`

`"Pre-tip" color(white)("d") +color(white)("dd") "tip "= "final cost"`
`color(white)("dd")color(red)(darr)color(white)("dddddd")color(red)(darr)color(white)("ddddd")color(red)(darr)`
`color(white)(".d")$38color(white)("dd")+color(white)("d")$7.60= $45.60`