Final answer:
To find the cost of a 16-ounce cup of orange juice, we can use the given information about the cost and volume of the 9-ounce and 12-ounce cups. The cost vs volume relationship is linear, so we can find the cost by finding the slope and using it to calculate the change in cost for the desired volume.
Step-by-step explanation:
To find the cost of a 16-ounce cup of orange juice, we can use the given information about the cost and volume of the 9-ounce and 12-ounce cups. We know that the cost vs volume relationship is linear, which means it can be represented by a straight line.
First, we need to find the slope of the line. The change in cost is $1.60 - $1.25 = $0.35, and the change in volume is 12 oz - 9 oz = 3 oz. So the slope is $0.35 / 3 oz = $0.1167 per oz.
Next, we can use the slope to find the cost of a 16-ounce cup. The change in volume from 12 oz to 16 oz is 16 oz - 12 oz = 4 oz. Multiplying the change in volume by the slope gives us the change in cost: 4 oz * $0.1167 per oz = $0.4668. Finally, we add the change in cost to the cost of the 12-ounce cup to get the cost of the 16-ounce cup: $1.60 + $0.4668 = $2.0668.