Use the image to answer the question.

An illustration shows Quadrant 1 of a coordinate plane. The x-axis is labeled Ounces and ranges from 0 to 40 in 5 unit increments. The y-axis is labeled Cost in dollars and ranges from 0.00 to 4.00 in increments of 0.50. The graph is titled Cost per Ounce. A line connects four points plotted on the graph. The coordinates of the plotted points are left parenthesis 0 comma 0 right parenthesis, left parenthesis 8 comma 0.80 right parenthesis, left parenthesis 15 comma 1.50 right parenthesis, and left parenthesis 30 comma 3.00 right parenthesis.

Store A and Store B are advertising canned corn on sale. Store A’s canned corn cost per ounce is displayed in the graph. Store B’s canned corn is represented by the equation y=0.13x
. Which store has the better buy and by how much?

1 answer

To compare the cost per ounce of canned corn from Store A and Store B, we need to evaluate the points from Store A's graph and the equation for Store B.

Store A's cost per ounce can be determined from the plotted points:

  • At \( x = 0 \) ounces, the cost \( y = 0.00 \) dollars.
  • At \( x = 8 \) ounces, the cost \( y = 0.80 \) dollars, so the cost per ounce is \( \frac{0.80}{8} = 0.10 \) dollars per ounce.
  • At \( x = 15 \) ounces, the cost \( y = 1.50 \) dollars, so the cost per ounce is \( \frac{1.50}{15} = 0.10 \) dollars per ounce.
  • At \( x = 30 \) ounces, the cost \( y = 3.00 \) dollars, so the cost per ounce is \( \frac{3.00}{30} = 0.10 \) dollars per ounce.

From the above evaluations, Store A's price per ounce is consistently \( 0.10 \) dollars.

Now, for Store B, the cost per ounce can be calculated using the equation \( y = 0.13x \). This equation directly gives the cost based on the number of ounces purchased.

For different values of \( x \):

  • For \( x = 8 \) ounces, the cost is \( y = 0.13(8) = 1.04 \) dollars, cost per ounce = \( \frac{1.04}{8} = 0.13 \) dollars per ounce.
  • For \( x = 15 \) ounces, the cost is \( y = 0.13(15) = 1.95 \) dollars, cost per ounce = \( \frac{1.95}{15} = 0.13 \) dollars per ounce.
  • For \( x = 30 \) ounces, the cost is \( y = 0.13(30) = 3.90 \) dollars, cost per ounce = \( \frac{3.90}{30} = 0.13 \) dollars per ounce.

Now, we compare the two stores:

  • Store A: \( 0.10 \) dollars per ounce.
  • Store B: \( 0.13 \) dollars per ounce.

Conclusion: Store A has the better buy, as its cost per ounce is lower by:

\( 0.13 - 0.10 = 0.03 \) dollars per ounce.

Therefore, Store A is better by 0.03 dollars (3 cents) per ounce.