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To solve the problem of selecting the correct table of values that fits the equation [tex]\( c = 3.5 \cdot b \)[/tex], where [tex]\( c \)[/tex] represents the cost in dollars and [tex]\( b \)[/tex] represents the number of loaves, let's examine each table one by one.
Table 1:
[tex]\[ \begin{array}{|c|c|} \hline \text{Loaves } (b) & \text{Cost } (c) \\ \hline -2 & -7 \\ \hline 0 & 0 \\ \hline 2 & 7 \\ \hline 2 & 14 \\ \hline \end{array} \][/tex]
Let's verify if each pair (loaves, cost) satisfies the equation [tex]\( c = 3.5 \cdot b \)[/tex]:
1. For [tex]\( b = -2 \)[/tex]: [tex]\( c = 3.5 \cdot (-2) = -7 \)[/tex] (This is correct).
2. For [tex]\( b = 0 \)[/tex]: [tex]\( c = 3.5 \cdot 0 = 0 \)[/tex] (This is correct).
3. For [tex]\( b = 2 \)[/tex]: [tex]\( c = 3.5 \cdot 2 = 7 \)[/tex] (This is correct).
4. For [tex]\( b = 2 \)[/tex]: [tex]\( c = 3.5 \cdot 2 = 7 \)[/tex] not 14 (14 is incorrect).
Since the last pair does not satisfy the equation, Table 1 is not viable.
Table 2:
[tex]\[ \begin{array}{|c|c|c|} \hline \text{Loaves } (b) & \text{Cost } (c) \\ \hline 0 & 0 \\ \hline 0.5 & 1.75 \\ \hline 1.5 & 3.5 \\ \hline 1.5 & 5.25 \\ \hline \end{array} \][/tex]
Let's verify if each pair (loaves, cost) satisfies the equation [tex]\( c = 3.5 \cdot b \)[/tex]:
1. For [tex]\( b = 0 \)[/tex]: [tex]\( c = 3.5 \cdot 0 = 0 \)[/tex] (This is correct).
2. For [tex]\( b = 0.5 \)[/tex]: [tex]\( c = 3.5 \cdot 0.5 = 1.75 \)[/tex] (This is correct).
3. For [tex]\( b = 1.5 \)[/tex]: [tex]\( c = 3.5 \cdot 1.5 = 5.25 \)[/tex] (Incorrect, should be 5.25).
Since not all pairs satisfy the equation, Table 2 is not viable.
Table 3:
[tex]\[ \begin{array}{|c|c|} \hline \text{Loaves } (b) & \text{Cost } (c) \\ \hline 0 & 0 \\ \hline 3 & 10.5 \\ \hline 6 & 21 \\ \hline 9 & 31.5 \\ \hline \end{array} \][/tex]
Let's verify if each pair (loaves, cost) satisfies the equation [tex]\( c = 3.5 \cdot b \)[/tex]:
1. For [tex]\( b = 0 \)[/tex]: [tex]\( c = 3.5 \cdot 0 = 0 \)[/tex] (This is correct).
2. For [tex]\( b = 3 \)[/tex]: [tex]\( c = 3.5 \cdot 3 = 10.5 \)[/tex] (This is correct).
3. For [tex]\( b = 6 \)[/tex]: [tex]\( c = 3.5 \cdot 6 = 21 \)[/tex] (This is correct).
4. For [tex]\( b = 9 \)[/tex]: [tex]\( c = 3.5 \cdot 9 = 31.5 \)[/tex] (This is correct).
Since all pairs in Table 3 satisfy the equation, Table 3 is the correct and viable table of values.
Therefore, the table of values that matches the equation and includes only viable solutions is:
[tex]\[ \begin{array}{|c|c|} \hline \text{Loaves } (b) & \text{Cost } (c) \\ \hline 0 & 0 \\ \hline 3 & 10.5 \\ \hline 6 & 21 \\ \hline 9 & 31.5 \\ \hline \end{array} \][/tex]
Table 1:
[tex]\[ \begin{array}{|c|c|} \hline \text{Loaves } (b) & \text{Cost } (c) \\ \hline -2 & -7 \\ \hline 0 & 0 \\ \hline 2 & 7 \\ \hline 2 & 14 \\ \hline \end{array} \][/tex]
Let's verify if each pair (loaves, cost) satisfies the equation [tex]\( c = 3.5 \cdot b \)[/tex]:
1. For [tex]\( b = -2 \)[/tex]: [tex]\( c = 3.5 \cdot (-2) = -7 \)[/tex] (This is correct).
2. For [tex]\( b = 0 \)[/tex]: [tex]\( c = 3.5 \cdot 0 = 0 \)[/tex] (This is correct).
3. For [tex]\( b = 2 \)[/tex]: [tex]\( c = 3.5 \cdot 2 = 7 \)[/tex] (This is correct).
4. For [tex]\( b = 2 \)[/tex]: [tex]\( c = 3.5 \cdot 2 = 7 \)[/tex] not 14 (14 is incorrect).
Since the last pair does not satisfy the equation, Table 1 is not viable.
Table 2:
[tex]\[ \begin{array}{|c|c|c|} \hline \text{Loaves } (b) & \text{Cost } (c) \\ \hline 0 & 0 \\ \hline 0.5 & 1.75 \\ \hline 1.5 & 3.5 \\ \hline 1.5 & 5.25 \\ \hline \end{array} \][/tex]
Let's verify if each pair (loaves, cost) satisfies the equation [tex]\( c = 3.5 \cdot b \)[/tex]:
1. For [tex]\( b = 0 \)[/tex]: [tex]\( c = 3.5 \cdot 0 = 0 \)[/tex] (This is correct).
2. For [tex]\( b = 0.5 \)[/tex]: [tex]\( c = 3.5 \cdot 0.5 = 1.75 \)[/tex] (This is correct).
3. For [tex]\( b = 1.5 \)[/tex]: [tex]\( c = 3.5 \cdot 1.5 = 5.25 \)[/tex] (Incorrect, should be 5.25).
Since not all pairs satisfy the equation, Table 2 is not viable.
Table 3:
[tex]\[ \begin{array}{|c|c|} \hline \text{Loaves } (b) & \text{Cost } (c) \\ \hline 0 & 0 \\ \hline 3 & 10.5 \\ \hline 6 & 21 \\ \hline 9 & 31.5 \\ \hline \end{array} \][/tex]
Let's verify if each pair (loaves, cost) satisfies the equation [tex]\( c = 3.5 \cdot b \)[/tex]:
1. For [tex]\( b = 0 \)[/tex]: [tex]\( c = 3.5 \cdot 0 = 0 \)[/tex] (This is correct).
2. For [tex]\( b = 3 \)[/tex]: [tex]\( c = 3.5 \cdot 3 = 10.5 \)[/tex] (This is correct).
3. For [tex]\( b = 6 \)[/tex]: [tex]\( c = 3.5 \cdot 6 = 21 \)[/tex] (This is correct).
4. For [tex]\( b = 9 \)[/tex]: [tex]\( c = 3.5 \cdot 9 = 31.5 \)[/tex] (This is correct).
Since all pairs in Table 3 satisfy the equation, Table 3 is the correct and viable table of values.
Therefore, the table of values that matches the equation and includes only viable solutions is:
[tex]\[ \begin{array}{|c|c|} \hline \text{Loaves } (b) & \text{Cost } (c) \\ \hline 0 & 0 \\ \hline 3 & 10.5 \\ \hline 6 & 21 \\ \hline 9 & 31.5 \\ \hline \end{array} \][/tex]
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