Final answer:
The ½ gallon jug of syrup should be sold for $1.06 to have the same unit rate as the 6-gallon jug priced at $12.72.
Step-by-step explanation:
To determine the price per half-gallon of syrup so that the unit rate is the same as a 6-gallon jug that costs $12.72, we first need to find the unit price per gallon of the larger jug. To do this, divide the total cost by the number of gallons. This gives us $12.72 ÷ 6 gallons = $2.12 per gallon. Now, since the question asks for the price of a ½ gallon jug, we multiply the per-gallon cost by ½.
$2.12 × ½ = $1.06
Therefore, the ½ gallon jug of syrup should be sold at $1.06 to maintain the same unit rate as the 6-gallon jug. It is important to note that this approach assumes that the cost scales linearly with the volume of the syrup, which is often the case for bulk purchases. To find the price at which a 1/2 gallon jug should be sold in order for the unit rate to be the same as a 6 gallon jug, we need to set up a proportion.
Let x be the price of the 1/2 gallon jug.
Therefore, the unit rate for the 6 gallon jug is 12.72/6 = 2.12/gallon.
The unit rate for the 1/2 gallon jug is x/0.5 = 2x/gallon.
Setting up the proportion:
2.12/gallon = 2x/gallon
Cross multiplying, we get:
2.12 * 0.5 = 2x
1.06 = 2x
x = 1.06/2
x = 0.53
Therefore, the 1/2 gallon jug should be sold at a price of $0.53 in order for the unit rate to be the same as the 6 gallon jug.