Question

lincoln was comparing the price of cranberry juice at two stores. lincoln can buy 16 bottles of cranberry juice at store b for a total cost of $11.20. the table below represents what lincoln would pay in dollars and cents, y, for x bottles of cranberry juice at store a.
store a

bottles (x)	total cost (y)
13	$3.77
18	$5.22
20	$5.80

how much less is a bottle of cranberry juice at store a than at store b?

Explanation:

Step1: Find unit price of Store B

To find the unit price (price per bottle) at Store B, we use the formula for unit price: $\text{Unit Price} = \frac{\text{Total Cost}}{\text{Number of Bottles}}$. For Store B, total cost is $\$11.20$ and number of bottles is 16. So, unit price of Store B is $\frac{11.20}{16}$.
Calculating that: $11.20\div16 = 0.7$ dollars per bottle.

Step2: Find unit price of Store A

We can use any row from the table of Store A to find the unit price. Let's take the first row: 10 bottles cost $\$2.90$. Using the same unit price formula, unit price of Store A is $\frac{2.90}{10}$.
Calculating that: $2.90\div10 = 0.29$ dollars per bottle. (We can verify with other rows, e.g., 20 bottles cost $\$5.80$, so $5.80\div20 = 0.29$ as well, so the unit price is consistent.)

Step3: Find the difference in unit prices

Now, we need to find how much less a bottle at Store A is than at Store B. So we subtract the unit price of Store A from that of Store B: $0.7 - 0.29$.
Calculating that: $0.7 - 0.29 = 0.41$ dollars.

Answer:

$\$0.41$