Question

A hairdresser is considering ordering a certain shampoo.  Company A charges $5 per 8 ounce bottle plus a $5 handling fee per order.  Company B charges $2 per 8 ounce bottle plus a $23 handling fee per order.  How many bottles must the hairdresser buy to justify using Company B?

Answer 1

For the shampoo:

Company A charges $5 per ounce bottle + $5 handling fee.

Company B charges $2 per ounce bottle + $23 handling fee.

Let C represent the total cost for the shampoo and x represent the number of bottles of shampoo then you can express the total cost for both companies as equations:

`\begin{gathered} C_A=5x+5 \\ C_B=8x+23 \end{gathered}`

For the hairdresser to justify using the shampoo of company C, the cost must be less than for company A, so that:

[tex]\begin{gathered} C_BNow