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's represent the cost for company A as C_A and the cost for company B as C_B.
C_A = $14 + $7p (where p represents the weight in pounds)
C_B = $15 + $6p
To find the weight at which both companies charge the same amount, we can set C_A equal to C_B:
$14 + $7p = $15 + $6p
Subtract $14 from both sides:
$7p = $1 + $6p
Subtract $6p from both sides:
$p = $1
So, at 1 pound, both companies will charge the same amount.
To find the equivalent cost at 1 pound, we can substitute $1 for p in either of the cost equations. Let's use C_A:
C_A = $14 + $7(1)
C_A = $14 + $7
C_A = $21
Therefore, the equivalent cost for 1 pound is $21.
So, the answer is:
G. 1 pound for $21