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?
To determine how many bottles the hairdresser must buy to justify using Company B, we need to compare the total cost of ordering from each company.
Let's assume the hairdresser wants to order x bottles of shampoo.
For Company A:
- The cost per bottle is $4.
- The handling fee per order is $10.
So, the total cost for Company A can be calculated as:
Total Cost (A) = (Cost per bottle × Number of bottles) + Handling fee
= 4x + 10
For Company B:
- The cost per bottle is $3.
- The handling fee per order is $25.
Therefore, the total cost for Company B can be calculated as:
Total Cost (B) = (Cost per bottle × Number of bottles) + Handling fee
= 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 need to find the value of x (number of bottles) that satisfies the inequality:
3x + 25 ≤ 4x + 10
Simplifying the inequality:
25 - 10 ≤ 4x - 3x
15 ≤ x
Therefore, the hairdresser must buy at least 15 bottles of shampoo to justify using Company B.