Question

damian was comparing the price of cranberry juice at two stores. damian can buy 7 bottles of cranberry juice at store b for a total cost of $3.29. the table below represents what damian would pay in dollars and cents, y, for x bottles of cranberry juice at store a. \
store a \

bottles (x)	total cost (y)	\
5	$8.35	\
8	$13.36	\
16	$26.72	\
20	$33.40	\

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

Explanation:

Step1: Find unit price of Store A

To find the unit price (price per bottle) at Store A, we can use any of the given data points. Let's take the first one: \( x = 5 \), \( y = 8.35 \). The unit price \( p_A \) is total cost divided by number of bottles, so \( p_A=\frac{8.35}{5} \)
\( p_A = 1.67 \) dollars per bottle. We can verify with another point, say \( x = 20 \), \( y = 33.40 \). Then \( \frac{33.40}{20}=1.67 \), so the unit price at Store A is $1.67.

Step2: Find unit price of Store B

At Store B, 7 bottles cost $3.29. So the unit price \( p_B=\frac{3.29}{7} \)
\( p_B = 0.47 \) dollars per bottle.

Step3: Find the difference

We need to find how much less a bottle at Store B is than at Store A. So we calculate \( p_A - p_B \)
\( 1.67 - 0.47 = 1.20 \)

Answer:

\( \$1.20 \)