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The number of loaves of bread purchased and the total cost of the bread in dollars can be modeled by the equation [tex]\( c = 3.5b \)[/tex]. Which table of values matches the equation and includes only viable solutions?

[tex]\[
\begin{tabular}{|c|c|}
\hline
Loaves $(b)$ & Cost $(c)$ \\
\hline
-2 & -7 \\
\hline
0 & 0 \\
\hline
2 & 7 \\
\hline
4 & 14 \\
\hline
\end{tabular}
\][/tex]

[tex]\[
\begin{tabular}{|c|c|}
\hline
Loaves $(b)$ & Cost $(c)$ \\
\hline
0 & 0 \\
\hline
0.5 & 1.75 \\
\hline
1 & 3.5 \\
\hline
1.5 & 5.25 \\
\hline
\end{tabular}
\][/tex]

[tex]\[
\begin{tabular}{|c|c|}
\hline
Loaves $(b)$ & Cost $(c)$ \\
\hline
0 & 0 \\
\hline
3 & 10.5 \\
\hline
6 & 21 \\
\hline
9 & 31.5 \\
\hline
\end{tabular}
\][/tex]

Sagot :

GinnyAnsweridn
To determine which table of values correctly corresponds to the equation [tex]\( c = 3.5b \)[/tex], we need to check each table to see if every value pair [tex]\((b, c)\)[/tex] satisfies the equation.

Let's examine each table one by one:

### Table 1
[tex]\[ \begin{array}{|c|c|} \hline \text{Loaves } (b) & \text{Cost } (c) \\ \hline -2 & -7 \\ 0 & 0 \\ 2 & 7 \\ 4 & 14 \\ \hline \end{array} \][/tex]

- For [tex]\( b = -2 \)[/tex], [tex]\( c = -7 \)[/tex]: [tex]\( 3.5 \times -2 = -7 \)[/tex]
- For [tex]\( b = 0 \)[/tex], [tex]\( c = 0 \)[/tex]: [tex]\( 3.5 \times 0 = 0 \)[/tex]
- For [tex]\( b = 2 \)[/tex], [tex]\( c = 7 \)[/tex]: [tex]\( 3.5 \times 2 = 7 \)[/tex]
- For [tex]\( b = 4 \)[/tex], [tex]\( c = 14 \)[/tex]: [tex]\( 3.5 \times 4 = 14 \)[/tex]

All pairs satisfy [tex]\( c = 3.5b \)[/tex].

### Table 2
[tex]\[ \begin{array}{|c|c|} \hline \text{Loaves } (b) & \text{Cost } (c) \\ \hline 0 & 0 \\ 0.5 & 1.75 \\ 1 & 3.5 \\ 1.5 & 5.25 \\ \hline \end{array} \][/tex]

- For [tex]\( b = 0 \)[/tex], [tex]\( c = 0 \)[/tex]: [tex]\( 3.5 \times 0 = 0 \)[/tex]
- For [tex]\( b = 0.5 \)[/tex], [tex]\( c = 1.75 \)[/tex]: [tex]\( 3.5 \times 0.5 = 1.75 \)[/tex]
- For [tex]\( b = 1 \)[/tex], [tex]\( c = 3.5 \)[/tex]: [tex]\( 3.5 \times 1 = 3.5 \)[/tex]
- For [tex]\( b = 1.5 \)[/tex], [tex]\( c = 5.25 \)[/tex]: [tex]\( 3.5 \times 1.5 = 5.25 \)[/tex]

All pairs satisfy [tex]\( c = 3.5b \)[/tex].

### Table 3
[tex]\[ \begin{array}{|c|c|} \hline \text{Loaves } (b) & \text{Cost } (c) \\ \hline 0 & 0 \\ 3 & 10.5 \\ 6 & 21 \\ 9 & 31.5 \\ \hline \end{array} \][/tex]

- For [tex]\( b = 0 \)[/tex], [tex]\( c = 0 \)[/tex]: [tex]\( 3.5 \times 0 = 0 \)[/tex]
- For [tex]\( b = 3 \)[/tex], [tex]\( c = 10.5 \)[/tex]: [tex]\( 3.5 \times 3 = 10.5 \)[/tex]
- For [tex]\( b = 6 \)[/tex], [tex]\( c = 21 \)[/tex]: [tex]\( 3.5 \times 6 = 21 \)[/tex]
- For [tex]\( b = 9 \)[/tex], [tex]\( c = 31.5 \)[/tex]: [tex]\( 3.5 \times 9 = 31.5 \)[/tex]

All pairs satisfy [tex]\( c = 3.5b \)[/tex].

### Conclusion
Since all the pairs in each of the three tables satisfy the equation [tex]\( c = 3.5b \)[/tex], all three tables match the equation and include only viable solutions. Therefore, the tables of values that match the equation [tex]\( c = 3.5b \)[/tex] are:

1. Table 1
2. Table 2
3. Table 3
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