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.

Question

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?

Answer 1

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.