Question

Eight pens cost $9.20. What is the unit price?

Answer 1

Unit price of pen is `$1.15`

Explanation:

As `8` pens cost `$9.20`

Unit price of pen is `$9.20/8=$1.15`

Answer 2

In support of Shwetank

The unit price (price of 1) is $1.15

Explanation:

Shwetanks method is the one every one uses ( including me ) once they have got used to this type of question and understand what is going on.

`color(blue)("Demonstrating where the shortcut method comes from")`

Using ratio method

We have 8 pens at a total cost of $9.20

Objective: To find the price of one pen (unit price)

As a ratio we have:`" "("cost")/("count of pens") -> ($9.20)/8`

But we need to change the 8 into 1. We can do this by adopting `8-:8`. However, to maintain proportionality what we do to the bottom of the ratio (for multiply or divide) we also do to the top. So we have:

`" "("cost")/("count of pens") -> ($9.20)/8-=($9.20-:8)/(8-:8) = ($1.15)/1`
`" "color(magenta)(uarr)`
`color(magenta)(" This is where the shortcut comes from.")`

So the unit price (price of 1) is $1.15