A table of values can be used to represent variables that are directly proportional.
The complete table of proportions is:
![\left[\begin{array}{ccccccccc}Letters&10&2&[150 ]&7&1&500&[420] \\Cost&0.45&0.90&6.75&[0.315]&[0.045 ]&[22.5 ] & 18.90\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccccccc%7DLetters%2610%262%26%5B150%20%5D%267%261%26500%26%5B420%5D%20%5C%5CCost%260.45%260.90%266.75%26%5B0.315%5D%26%5B0.045%20%5D%26%5B22.5%20%5D%20%26%2018.90%5Cend%7Barray%7D%5Cright%5D)
Given that
![\left[\begin{array}{ccccccccc}Letters&10&2&[\ ]&7&1&500&[\ ] \\Cost&0.45&0.90&6.75&[\ ]&[\ ]&[\ ] & 18.90\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccccccc%7DLetters%2610%262%26%5B%5C%20%5D%267%261%26500%26%5B%5C%20%5D%20%5C%5CCost%260.45%260.90%266.75%26%5B%5C%20%5D%26%5B%5C%20%5D%26%5B%5C%20%5D%20%26%2018.90%5Cend%7Barray%7D%5Cright%5D)
Let:
<em />
<em> Letters</em>
<em />
<em> Cost</em>
<em />
Using proportional reasoning, we have:

Where
<em />
<em> ratio of proportion</em>
For the first values of C and L, we have:


Divide both sides by 10

So, the equation of proportion is:

<u>When C = 6.75, we have:</u>


Solve for L


<u>When L = 7, we have:</u>



<u>When L = 1, we have:</u>



<u>When L = 500, we have:</u>



<u>When C = 18.90, we have:</u>


Solve for L


Hence, the complete table is:
![\left[\begin{array}{ccccccccc}Letters&10&2&[150 ]&7&1&500&[420] \\Cost&0.45&0.90&6.75&[0.315]&[0.045 ]&[22.5 ] & 18.90\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccccccc%7DLetters%2610%262%26%5B150%20%5D%267%261%26500%26%5B420%5D%20%5C%5CCost%260.45%260.90%266.75%26%5B0.315%5D%26%5B0.045%20%5D%26%5B22.5%20%5D%20%26%2018.90%5Cend%7Barray%7D%5Cright%5D)
Read more about proportions at:
brainly.com/question/21126582