To determine the viable solutions for the number of books \( b \) that Mr. Hann orders and the total weight \( w \) in ounces, we can use the relationship given in the problem: each book weighs 6 ounces. Therefore, the total weight \( w \) of \( b \) books is \( w = 6b \).
Let's consider different tables of possible (b, w) values and check for viability.
### Table 1
\[
\begin{array}{|c|c|}
\hline
b & w \\
\hline
1 & 6 \\
2 & 12 \\
3 & 18 \\
4 & 24 \\
\hline
\end{array}
\]
### Table 2
\[
\begin{array}{|c|c|}
\hline
b & w \\
\hline
1 & 7 \\
2 & 13 \\
3 & 18 \\
4 & 25 \\
\hline
\end{array}
\]
### Table 3
\[
\begin{array}{|c|c|}
\hline
b & w \\
\hline
1 & 6 \\
2 & 11 \\
3 & 17 \\
4 & 23 \\
\hline
\end{array}
\]
### Table 4
\[
\begin{array}{|c|c|}
\hline
b & w \\
\hline
1 & 6 \\
2 & 12 \\
3 & 18 \\
4 & 24 \\
5 & 30 \\
\hline
\end{array}
\]
To determine which tables contain only viable solutions, we simply need to check if \( w = 6b \) for each pair \((b, w)\).
- **Table 1:** Viable because \( w = 6b \) for all rows.
- **Table 2:** Not viable. For \( b = 1 \), \( w \neq 6 \times 1 \); for \( b = 2 \), \( w \neq 6 \times 2 \), for \( b = 4 \), \( w \neq 6 \times 4 \).
- **Table 3:** Not viable. For \( b = 2 \), \( w \neq 6 \times 2 \); for \( b = 3 \), \( w \neq 6 \times 3 \); for \( b = 4 \), \( w \neq 6 \times 4 \).
- **Table 4:** Viable because \( w = 6b \) for all rows.
### Conclusion
The tables that contain only viable solutions are **Table 1 and Table 4**.
Mr. Hann is trying to decide how many new copies of a book to order for his students. Each book weighs 6 ounces.
Which table contains only viable solutions if b represents the number of books he orders and w represents the total weight of the books, in ounces?
1 answer