Question

A café sells peach smoothies and berry smoothies. The café makes a profit of $2.25 for each peach smoothie that is sold and a profit of $2 for each berry smoothie that is sold. The owner of the café wants to make a total profit of more than $90 per day from the sales of smoothies.

a. Write an inequality that represents the number of peach smoothies p and berry smoothies b that the café needs to sell. Describe the constraints on the variables.

Answer 1

To achieve a profit goal of more than $90 a day, the café must sell peach and berry smoothies according to the inequality 2.25p + 2b > 90, where p and b are the numbers of peach and berry smoothies sold. Both p and b must be non-negative integers and within practical limits.

Step-by-step explanation:

The question being asked involves setting up an inequality to represent a business scenario for a café. The café makes a certain amount of profit for each smoothie that is sold, and we want to determine how many of each type of smoothie need to be sold to achieve a specific profit goal.

We are given that the profit per peach smoothie (p) is $2.25 and the profit per berry smoothie (b) is $2. The owner wants to make more than $90 per day from selling these smoothies. This scenario can be described by the inequality 2.25p + 2b > 90, where p is the number of peach smoothies and b is the number of berry smoothies sold.

The constraints on the variables are that both p and b must be non-negative integers since you cannot sell a negative number or fraction of a smoothie. Additionally, to apply this inequality to actual sales scenarios, both p and b must also adhere to practical limits, such as inventory and demand.