My grandmother needs to find the
best company to deliver a package.
Company A charges a fee of $14 plus $7
per pound. Company B charges a fee of
$15 plus $6 per pound. At what weight
will the companies charge the same
amount and what is the equivalent cost?
F. 2 pounds for $28
G. 1 pound for $21
H. 0.5 pound for $18
Let x represent the weight of the package in pounds.
The total cost for Company A is: C(x) = 14 + 7x
The total cost for Company B is: C(x) = 15 + 6x
To find the weight at which the companies charge the same amount, we set the two equations equal to each other:
14 + 7x = 15 + 6x
Subtract 6x from both sides:
14 + x = 15
Subtract 14 from both sides:
x = 1
Therefore, the weight at which the companies charge the same amount is 1 pound.
Now we can find the equivalent cost for this weight.
For Company A (x=1):
C(x) = 14 + 7(1) = $21
For Company B (x=1):
C(x) = 15 + 6(1) = $21
So for a 1-pound package, both companies will charge $21.
Answer:
G. 1 pound for $21