Certainly! Let's fill in the missing values in the table step-by-step using proportional reasoning.
1. Calculate the cost per letter:
From the given pairs:
- 10 letters cost 4.50 units
- 2 letters cost 0.90 units
- 5 letters cost 6.75 units
We recognize that the cost is proportional to the number of letters. Hence, we can calculate the cost per letter using the first given pair (10 letters for 4.50 units):
Cost per letter [tex]\( = \frac{4.50}{10} = 0.45 \)[/tex] units per letter.
2. Fill in the cost for 7 letters:
Using the cost per letter:
Cost for 7 letters [tex]\( = 7 \times 0.45 = 3.15 \)[/tex] units.
3. Fill in the cost for 1 letter:
Using the cost per letter:
Cost for 1 letter [tex]\( = 1 \times 0.45 = 0.45 \)[/tex] units.
4. Fill in the cost for 500 letters:
Using the cost per letter:
Cost for 500 letters [tex]\( = 500 \times 0.45 = 225.00 \)[/tex] units.
5. Find the number of letters for a given cost of 18.90 units:
We need to find how many letters would cost 18.90 units. We can use the cost per letter for this:
Number of letters for 18.90 units [tex]\( = \frac{18.90}{0.45} = 42 \)[/tex] letters.
(Note: The precise calculation is approximately 41.99999999999999, which we round to the nearest whole number as we're dealing with whole letters.)
Now, we can complete the table:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Number of Letters} & \text{Cost of stamps (units)} \\
\hline
10 & 4.50 \\
\hline
2 & 0.90 \\
\hline
5 & 6.75 \\
\hline
7 & 3.15 \\
\hline
1 & 0.45 \\
\hline
500 & 225.00 \\
\hline
42 & 18.90 \\
\hline
\end{array}
\][/tex]
This table is now complete, showing the cost of sending a certain number of letters through the mail.
