To find out how much more expensive it is to buy salmon at SuperGrocery A than at SuperGrocery B, we first need to calculate the price per pound of salmon at both stores.
Step 1: Calculate the price per pound at SuperGrocery B
At SuperGrocery B, the cost for 3 pounds of salmon is $24.63.
\[ \text{Price per pound at SuperGrocery B} = \frac{\text{Total cost}}{\text{Total pounds}} = \frac{24.63}{3} \approx 8.21 \]
So, the price per pound at SuperGrocery B is approximately $8.21.
Step 2: Calculate the price per pound at SuperGrocery A
Now let's find the price per pound at SuperGrocery A based on the provided costs.
- For \(x = 2\) pounds, \(y = 23.70\):
\[ \text{Price per pound for 2 pounds} = \frac{23.70}{2} = 11.85 \]
- For \(x = 2.5\) pounds, \(y = 29.63\):
\[ \text{Price per pound for 2.5 pounds} = \frac{29.63}{2.5} = 11.852 \]
- For \(x = 3.5\) pounds, \(y = 41.48\):
\[ \text{Price per pound for 3.5 pounds} = \frac{41.48}{3.5} \approx 11.87 \]
- For \(x = 4.5\) pounds, \(y = 53.33\):
\[ \text{Price per pound for 4.5 pounds} = \frac{53.33}{4.5} \approx 11.85 \]
Step 3: Average price per pound at SuperGrocery A
From our calculations, the price per pound is approximately \(11.85\) for 2, 4.5 pounds, and \(11.87\) for 3.5 pounds and \(11.852\) for 2.5 pounds. This suggests the per-pound costs at SuperGrocery A are consistently around \(11.85 - 11.87\).
Step 4: Calculate the difference
Now we will compare the price per pound at SuperGrocery A and SuperGrocery B:
\[ \text{Difference in price per pound} = \text{Price per pound at SuperGrocery A} - \text{Price per pound at SuperGrocery B} \] \[ \text{Difference} = 11.85 - 8.21 \approx 3.64 \]
Therefore, it is approximately $3.64 more expensive per pound to buy salmon at SuperGrocery A than at SuperGrocery B.