My grandmother needs to find the best company to deliver her 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?
the answer is 1 pound for $21. Show your work for how this answer is correct.
Let x be the weight of the package in pounds.
For Company A: cost = 14 + 7x
For Company B: cost = 15 + 6x
To find when the companies charge the same amount, we can set the two equations equal to each other:
14 + 7x = 15 + 6x
Subtracting 6x from both sides:
14 + x = 15
Subtracting 14 from both sides:
x = 1
So the companies will charge the same amount at 1 pound.
Substitute x = 1 back into the equation to find the equivalent cost:
For Company A: cost = 14 + 7(1) = 14 + 7 = $21
For Company B: cost = 15 + 6(1) = 15 + 6 = $21
Therefore, the equivalent cost for both companies at 1 pound is $21.