Let's go through each part of the question step-by-step and find the required solutions.
1. Cost of a 7-pound package:
[tex]\[
c = 229 \cdot 7 + 14.33 = 1603 + 14.33 = 1617.33
\][/tex]
So, the cost of a 7-pound package is [tex]$1617.33.
2. Cost of a 13-pound package:
\[
c = 229 \cdot 13 + 14.33 = 2977 + 14.33 = 2991.33
\]
So, the cost of a 13-pound package is $[/tex]2991.33.
3. Cost of a 14-pound package:
[tex]\[
c = 229 \cdot 14 + 14.33 = 3206 + 14.33 = 3220.33
\][/tex]
So, the cost of a 14-pound package is [tex]$3220.33.
4. Cost of a 15.5-pound package:
\[
c = 229 \cdot 15.5 + 14.33 = 3559.5 + 14.33 = 3573.83
\]
So, the cost of a 15.5-pound package is $[/tex]3563.83. Given the cost options, we need to choose the approximate cost:
- Option A: [tex]$36 is much lower than $[/tex]3573.83.
- Option B: [tex]$67 is still significantly lower than $[/tex]3573.83.
- Option C: [tex]$50 is in the vicinity of $[/tex]3573.83.
However, since the provided result is not close to any of these options, we identify the closest provided option as [tex]$36.
Therefore, the approximate cost of sending a $[/tex]15 \frac{1}{2}[tex]$-pound package is $[/tex]36 (from the given choices).
5. Weight for a given cost of [tex]$17119:
We rearrange the formula \( c = 229w + 14.33 \) to solve for \( w \):
\[
w = \frac{c - 14.33}{229}
\]
Substituting \( c = 17119 \):
\[
w = \frac{17119 - 14.33}{229} = \frac{17104.67}{229} \approx 74.7
\]
When rounded to the nearest pound, the weight is approximately 75 pounds.
So, the detailed solutions to the given questions are:
1. A 7-pound package costs $[/tex]1617.33.
2. A 13-pound package costs [tex]$2991.33.
3. A 14-pound package costs $[/tex]3220.33.
4. The approximate cost of sending a [tex]$15 \frac{1}{2}$[/tex]-pound package is [tex]$36.
5. A package that costs $[/tex]17119 to mail weighs about 75 pounds.
