Question
Caroline was comparing the price of salmon at two stores. At SuperGrocery B, 3 pounds of salmon costs $24.63. The table below represents the total cost, in dollars and cents, y, that it costs for xx pounds of salmon at SuperGrocery A.
SuperGrocery A
Pounds left parenthesis x right parenthesisPounds (x) Total Cost left parenthesis y right parenthesisTotal Cost (y)
22 dollar sign, 23, point, 7, 0$23.70
2, point, 52.5 dollar sign, 29, point, 6, 3$29.63
3, point, 53.5 dollar sign, 41, point, 4, 8$41.48
4, point, 54.5 dollar sign, 53, point, 3, 3$53.33
How much more expensive is it, per pound, to buy salmon at SuperGrocery A than at SuperGrocery B?
SuperGrocery A
Pounds left parenthesis x right parenthesisPounds (x) Total Cost left parenthesis y right parenthesisTotal Cost (y)
22 dollar sign, 23, point, 7, 0$23.70
2, point, 52.5 dollar sign, 29, point, 6, 3$29.63
3, point, 53.5 dollar sign, 41, point, 4, 8$41.48
4, point, 54.5 dollar sign, 53, point, 3, 3$53.33
How much more expensive is it, per pound, to buy salmon at SuperGrocery A than at SuperGrocery B?
Answers
GPT-4o mini
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.
1. For \(x = 2\) pounds, \(y = 23.70\):
\[
\text{Price per pound for 2 pounds} = \frac{23.70}{2} = 11.85
\]
2. For \(x = 2.5\) pounds, \(y = 29.63\):
\[
\text{Price per pound for 2.5 pounds} = \frac{29.63}{2.5} = 11.852
\]
3. For \(x = 3.5\) pounds, \(y = 41.48\):
\[
\text{Price per pound for 3.5 pounds} = \frac{41.48}{3.5} \approx 11.87
\]
4. 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.
### 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.
1. For \(x = 2\) pounds, \(y = 23.70\):
\[
\text{Price per pound for 2 pounds} = \frac{23.70}{2} = 11.85
\]
2. For \(x = 2.5\) pounds, \(y = 29.63\):
\[
\text{Price per pound for 2.5 pounds} = \frac{29.63}{2.5} = 11.852
\]
3. For \(x = 3.5\) pounds, \(y = 41.48\):
\[
\text{Price per pound for 3.5 pounds} = \frac{41.48}{3.5} \approx 11.87
\]
4. 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.