A hairdresser is considering ordering a certain shampoo. Company A charges $4 per 8-oz bottle plus a $10 handling fee per order. Company B charges $3 per 8-oz bottle plus a $25 handling fee per order. How many bottles must the hairdresser buy to justify using company B.
once is enough, please ...
To Anonymous, my first has typographical error, so I submitted again the correct one. I hope you understand, besides you did not answer either of my two questions.
To find out how many bottles the hairdresser must buy to justify using Company B over Company A, we need to compare the total cost of purchasing from each company.
Let's break down the costs of purchasing from each company:
For Company A:
- Cost per bottle: $4
- Handling fee per order: $10
For Company B:
- Cost per bottle: $3
- Handling fee per order: $25
Now, let's assume the hairdresser wants to purchase x bottles:
Total cost from Company A:
Cost of x bottles from Company A = Cost per bottle x Number of bottles
= $4 x x = $4x
Total cost from Company B:
Cost of x bottles from Company B = Cost per bottle x Number of bottles + Handling fee per order
= $3 x x + $25 = $3x + $25
To justify using Company B, the total cost from Company B should be less than or equal to the total cost from Company A.
So, we can set up the following inequality:
$3x + $25 ≤ $4x
Now, let's solve the inequality:
$25 ≤ $4x - $3x
$25 ≤ x
This means that the hairdresser must buy at least 25 bottles from Company B to justify using it over Company A.