Consider both companies separately. Find the rates that compare the price to the number of gallons of lemonade. Then, simplify the the rates to get the unit prices. Note that we need to change the units for the second company.
Sweet and Sour Company, see solution.
Practice makes perfect
We are told that the Lovin' Lemon Company sells a 4-gallon jug of lemonade for $24. The Sweet and Sour Company sells an eight-pack of 1-quart bottles of lemonade for $16. We want to determine which company has a higher unit price. We will find the unit prices one at a time.
Lovin' Lemon Company
We know that the Lovin' Lemon Company sells a 4-gallon jug of lemonade for $24. We can use this information to write a rate that compares the price to the number of gallons. To do so, we need to divide the given price by the number of gallons in a jug.
$24/4gallons
We want to know the unit price. We can find this by simplifying our rate to the form of a unit rate. Unit rates have a denominator of 1 unit when the rate is written as a fraction. We can divide both the numerator and denominator of the our fraction by the value in the denominator, 4, to find our unit rate. Let's do it!
We get that the unit price for the Lovin' Lemon Company is $6 per 1 gallon of lemonade.
Sweet and Sour Company
The Sweet and Sour Company sells an eight-pack of 1-quart bottles of lemonade for $16. We want to compare the unit prices, so let's change the units. We know that 1 quart is 14 of a gallon. To convert quarts into gallons, we can multiply the number of quarts in a bottle, 1, by 14. We also need to multiply the result by 8 since there are 8 bottles in the package.
We can say that the Sweet and Sour Company offers 2 gallons of lemonade for $16. Now let's write a rate comparing the price to the number of gallons. To do so, we need to divide the given price by the number of gallons offered by the company.
$16/2gallons
Now let's simplify the rate to find the unit price. We will divide both the numerator and denominator of the rate by the value in the denominator, 2. Let's do it!
We get that the unit price for the Sweet and Sour Company is $8 per 1 gallon of lemonade.
Comparison
We have found that the unit price for the Lovin' Lemon Company is $6 per gallon of lemonade, while the unit price for the Sweet and Sour Company is $8 per gallon of lemonade. Therefore, the Sweet and Sour Company has a higher unit price than the Lovin' Lemon Company.
