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.

\frac{$ 2 4}{4 gallons}

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!

\frac{$ 2 4}{4 gallons}

ReduceFrac

$\frac{a}{b} = \frac{a / 4}{b / 4}$

\frac{$ 2 4 \div 4}{4 gallons \div 4}

CalcQuot

Calculate quotient

\frac{$ 6}{1 gallon}

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

\frac{1}{4}

of a gallon. To convert quarts into gallons, we can multiply the number of quarts in a bottle,

1,

by

\frac{1}{4} .

We also need to multiply the result by

8

since there are

8

bottles in the package.

1 \cdot \frac{1}{4} \cdot 8

OneMult

$1 \cdot a = a$

\frac{1}{4} \cdot 8

MoveRightFacToNumOne

$\frac{1}{b} \cdot a = \frac{a}{b}$

\frac{8}{4}

CalcQuot

Calculate quotient

2

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.

\frac{$ 1 6}{2 gallons}

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!

\frac{$ 1 6}{2 gallons}

ReduceFrac

$\frac{a}{b} = \frac{a / 2}{b / 2}$

\frac{$ 1 6 \div 2}{2 gallons \div 2}

CalcQuot

Calculate quotient

\frac{$ 8}{1 gallon}

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.

Exercise