Answer :
To solve this problem, we need to determine the price per quart for each container size and then find the ratio of the prices per quart.
### Step-by-Step Solution:
1. Calculate the price per quart for the 2-quart container:
The cost of a 2-quart container is [tex]$3.00. The volume of the 2-quart container is 2 quarts. \[ \text{Price per quart for the 2-quart container} = \frac{\$[/tex]3.00}{2 \, \text{quarts}} = \[tex]$1.50 \, \text{per quart} \] 2. Calculate the price per quart for the 1.5-quart container: The cost of a 1.5-quart container is $[/tex]2.50.
The volume of the 1.5-quart container is 1.5 quarts.
[tex]\[ \text{Price per quart for the 1.5-quart container} = \frac{\$2.50}{1.5 \, \text{quarts}} \approx \$1.67 \, \text{per quart} \][/tex]
3. Calculate the ratio of the price per quart of the 2-quart container to the price per quart of the 1.5-quart container:
[tex]\[ \text{Ratio} = \frac{\$1.50 \, \text{per quart}}{\$1.67 \, \text{per quart}} \approx 0.90 \][/tex]
4. Express the ratio in fractional form:
[tex]\[ 0.90 = \frac{9}{10} \][/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:
[tex]\[ \boxed{\frac{9}{10}} \][/tex]
So, the correct answer is Option A: [tex]\(\frac{9}{10}\)[/tex].
### Step-by-Step Solution:
1. Calculate the price per quart for the 2-quart container:
The cost of a 2-quart container is [tex]$3.00. The volume of the 2-quart container is 2 quarts. \[ \text{Price per quart for the 2-quart container} = \frac{\$[/tex]3.00}{2 \, \text{quarts}} = \[tex]$1.50 \, \text{per quart} \] 2. Calculate the price per quart for the 1.5-quart container: The cost of a 1.5-quart container is $[/tex]2.50.
The volume of the 1.5-quart container is 1.5 quarts.
[tex]\[ \text{Price per quart for the 1.5-quart container} = \frac{\$2.50}{1.5 \, \text{quarts}} \approx \$1.67 \, \text{per quart} \][/tex]
3. Calculate the ratio of the price per quart of the 2-quart container to the price per quart of the 1.5-quart container:
[tex]\[ \text{Ratio} = \frac{\$1.50 \, \text{per quart}}{\$1.67 \, \text{per quart}} \approx 0.90 \][/tex]
4. Express the ratio in fractional form:
[tex]\[ 0.90 = \frac{9}{10} \][/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:
[tex]\[ \boxed{\frac{9}{10}} \][/tex]
So, the correct answer is Option A: [tex]\(\frac{9}{10}\)[/tex].
