Question

Josiah went to the local barber to get his hair cut. It cost $18 for the haircut. Josiah tipped the barber 15%. What was the total cost of the haircut including the tip?

Answer 1

Total cost is $20.70.

Explanation:

Firstly, we must find the cost of the tip. To do this, we need to find 15% of $18. 15% means 15 per 100 (aka: 0.15). 'Of' in mathematics means multiplication. So..

`0.15*18=$2.70`

Now that we know the cost of the tip, we just need to add it to the cost of the haircut.

`18+2.70=$20.70` (total cost of haircut & tip)

And that's your final answer!

Answer 2

Another approach

`$20.70`

Explanation:

`color(Red)(115/100xx$18=$20.70)`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(green)("Idea behind the calculation method")`

`color(blue)("Concept 1")`

Percent is parts of a hundred. Basically it is a fraction where the denominator is fixed at 100.

So another way of writing 15% is `15/100`

So 15% of some quantity is the same as `15/100xx" some quantity"`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(blue)("Concept 2")`

Multiply any count by 1 and you do not change the value.

This is because, in words, you are saying you have 1 of them

So `1xx "something"` is saying you have 1 of it

`color(brown)("But 1 can be written in many ways, say, "100/100)`

The cut and tip is all of the $18 (1 of it) and `15/100` parts of it more

So in fact you are paying `(100/100 + 15/100)xx$18`

So you are paying `115/100xx$18 = $20.70`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Compare to an another method")`

`$18+(15/100 xx$18) = $18+$2.70`

`=$20.70`