A company sells ice cream in 2-quart containers for [tex]$\[tex]$3.00$[/tex][/tex] per container. The company also sells ice cream in 1.5-quart containers for [tex]$\[tex]$2.50$[/tex][/tex] per container. What is the ratio of the price per quart for the 2-quart container to the price per quart for the 1.5-quart container?

A. [tex]\frac{9}{10}[/tex]
B. [tex]\frac{10}{9}[/tex]
C. [tex]\frac{3}{2}[/tex]
D. [tex]\frac{5}{3}[/tex]
E. [tex]\frac{5}{2}[/tex]



Answer :

To solve the problem, we need to find the ratio of the price per quart for the 2-quart container to the price per quart for the 1.5-quart container. Here are the steps:

1. Determine the price per quart for the 2-quart container:

- The total price for a 2-quart container is $3.00.
- To find the price per quart, divide the total price by the number of quarts:
[tex]\[ \text{Price per quart for the 2-quart container} = \frac{3.00}{2} = 1.5 \text{ dollars per quart} \][/tex]

Therefore, the price per quart for the 2-quart container is \( 1.5 \) dollars.

2. Determine the price per quart for the 1.5-quart container:

- The total price for a 1.5-quart container is $2.50.
- To find the price per quart, divide the total price by the number of quarts:
[tex]\[ \text{Price per quart for the 1.5-quart container} = \frac{2.50}{1.5} \approx 1.6667 \text{ dollars per quart} \][/tex]

Therefore, the price per quart for the 1.5-quart container is approximately \( 1.6667 \) dollars.

3. Calculate the ratio of the price per quart for the 2-quart container to the price per quart for the 1.5-quart container:

- Let's denote the price per quart for the 2-quart container as \( P_2 \) and the price per quart for the 1.5-quart container as \( P_{1.5} \).
- Hence, \( P_2 = 1.5 \) and \( P_{1.5} \approx 1.6667 \).
- The ratio \( R \) is given by:
[tex]\[ R = \frac{P_2}{P_{1.5}} = \frac{1.5}{1.6667} \approx 0.9 \][/tex]

Therefore, the ratio of the price per quart for the 2-quart container to the price per quart for the 1.5-quart container is approximately \( 0.9 \).

4. Convert the ratio to a fractional form:

- \( 0.9 \) can be written as \( \frac{9}{10} \).

Therefore, the correct answer is [tex]\( A. \frac{9}{10} \)[/tex].