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A delivery company's charge for an overnight package weighing in excess of one pound is given by the formula [tex]\( c = 229w + 14.33 \)[/tex], where [tex]\( w \)[/tex] is the weight of the package in pounds. Find the following:

1. A 7-pound package costs [tex]\( \$30.36 \)[/tex] to send overnight. (Round to the nearest cent.)
2. A 13-pound package costs [tex]\( \$44.10 \)[/tex] to send overnight. (Round to the nearest cent.)
3. A 14-pound package costs [tex]\( \$46.39 \)[/tex] to send overnight. (Round to the nearest cent.)

The figure, shown to the right, is the graph of the formula for the company's charge, with [tex]\( w \)[/tex] on the horizontal axis, in pounds, and [tex]\( c \)[/tex] on the vertical axis, in dollars.

Choose the approximate cost of sending a [tex]\( 15 \frac{1}{2} \)[/tex]-pound package overnight.
A. [tex]\( \$36 \)[/tex]
B. [tex]\( \$67 \)[/tex]
C. [tex]\( \$50 \)[/tex]

A package that costs [tex]\( \$171.19 \)[/tex] to mail weighs about [tex]\( \square \)[/tex] pounds. (Round to the nearest pound.)


Sagot :

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.