# You put 500 pieces of paper in a copy machine. When you check back 6 days later, there are only 320 pieces left. How many pieces of paper are being used each day?

Oct 30, 2016

The mean usage over 6 days is 30 per day

#### Explanation:

Realistically you do not know. One day may use more than another. For example: they may all have been used on day 5 and none on all the other days.

The mean (average) use is all you can determine.

$\textcolor{b l u e}{\text{Determine total count of used pieces of paper}}$

${\cancel{5}}^{4} {\cancel{0}}^{10} 0$
$\underline{3 \textcolor{w h i t e}{. .} 2 \textcolor{w h i t e}{. .} 0} \text{ "larr" subtract}$
$1 \textcolor{w h i t e}{. .} 8 \textcolor{w h i t e}{. .} 0 \text{ "larr" total used}$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Determine the mean use per day}}$

Using ratio in fraction format

" "("Paper count")/("day count")->180/6

This is for 6 days but we need the count for 1 day

With ratio what you do to the bottom you also do to the top for multiply or divide. This maintains the correct proportions.

" "("Paper count")/("day count")->(180-:6)/(6-:6) = 30/1

So the $\underline{\text{mean}}$ usage over 6 days is 30 for each day