To find the ratio of the weight of the container to the weight of the contents, follow these steps:
1. Calculate the weight of the container:
The weight of the container accounts for [tex]\(\frac{13}{16}\)[/tex] of the total weight. Given the total weight is 48 pounds, we can calculate the weight of the container as follows:
[tex]\[
\text{Weight of the container} = \frac{13}{16} \times 48 = \frac{13 \times 48}{16}
\][/tex]
Simplify the fraction inside the multiplication first:
[tex]\[
\frac{48}{16} = 3
\][/tex]
Now multiply:
[tex]\[
\text{Weight of the container} = 13 \times 3 = 39 \text{ pounds}
\][/tex]
2. Calculate the weight of the contents:
Subtract the weight of the container from the total weight:
[tex]\[
\text{Weight of the contents} = 48 - 39 = 9 \text{ pounds}
\][/tex]
3. Calculate the ratio of the weight of the container to the weight of the contents:
The ratio is given by:
[tex]\[
\text{Ratio} = \frac{\text{Weight of the container}}{\text{Weight of the contents}} = \frac{39}{9}
\][/tex]
4. Identify the correct fraction from the given options:
The possible options were:
- [tex]\(\frac{9}{39}\)[/tex]
- [tex]\(\frac{9}{30}\)[/tex]
- [tex]\(\frac{30}{48}\)[/tex]
- [tex]\(\frac{39}{9}\)[/tex]
- [tex]\(\frac{48}{9}\)[/tex]
From our calculation, the ratio of the weight of the container to the weight of the contents is [tex]\(\frac{39}{9}\)[/tex].
Thus, the fraction that represents the ratio of the weight of the container to the weight of the contents is [tex]\(\boxed{\frac{39}{9}}\)[/tex].
