Make a table to answer Problems 27–28. (3-5)
Two shipping companies charge different amounts to mail packages. Company A
charges an initial $5 fee, and each pound shipped is an additional $1. Company B
charges an initial $3 fee, and $1.50 for each pound shipped.
27. At what weight will the two companies have the same charge?
28. Which company charges less for a 6-lb package? How much will you save?
Company A
$5+$1 per pound
Company B
$3 + 1.50 per pound
27.
3+1.50x=5+1x
1.50x=2+x
.50x=2
X=4
28.
6 lb package with company a
$5+($1x6)=$11
6lb package with company b
$3+($1.50x6)=$3+$9=$12
Company A charges less. You save $1
To create a table to answer Problems 27-28, we can compare the charges for different weights of packages for both Company A and Company B.
Let's begin by listing the weights of the packages in the first column of the table. We will use the weights 1 lb, 2 lb, 3 lb, 4 lb, 5 lb, and 6 lb for convenience.
Table:
| Weight (in pounds) | Company A Charge | Company B Charge |
|--------------------|-----------------|-----------------|
| 1 lb | $6 | $4.50 |
| 2 lb | $7 | $6.00 |
| 3 lb | $8 | $7.50 |
| 4 lb | $9 | $9.00 |
| 5 lb | $10 | $10.50 |
| 6 lb | $11 | $12.00 |
Now, let's answer the specific questions:
27. To determine at what weight the two companies have the same charge, we look for the row in the table where both Company A and Company B have the same charge. From the table, we can see that at 4 pounds, both companies have a charge of $9. Therefore, the two companies have the same charge at a weight of 4 pounds.
28. To determine which company charges less for a 6-lb package, we compare the charges in the table. From the table, we can see that Company A charges $11 for a 6-lb package, while Company B charges $12. Therefore, Company A charges less for a 6-lb package. The savings can be calculated by finding the difference between the charges, which is $12 - $11 = $1. Thus, you will save $1 by choosing Company A for a 6-lb package.