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?
To find the weight at which the companies charge the same amount, we can set up an equation:
Company A: $14 + $7x (x being the weight in pounds)
Company B: $15 + $6x
Setting them equal to each other:
$14 + $7x = $15 + $6x
$14 + $7x - $6x = $15 + $6x - $6x
$14 + x = $15
x = $1
Therefore, at a weight of 1 pound, both companies will charge the same amount.
To find the equivalent cost, we can substitute this weight back into either equation:
Company A: $14 + $7(1) = $14 + $7 = $21
Company B: $15 + $6(1) = $15 + $6 = $21
Therefore, both companies will charge $21 for a 1-pound package.