Question

An online furniture store sells chairs for $150 each and tables for $400 each. Every day, the store can ship no more than 30 pieces of furniture and must sell a minimum of $6500 worth of chairs and tables. If 10 tables were sold, determine the minimum number of chairs that the the store must sell in order to meet the requirements. If there are no possible solutions, submit an empty answer.

Answer 1

The online furniture store must sell a minimum of 20 chairs in order to meet the requirements.

Step-by-step explanation:

To determine the minimum number of chairs that the online furniture store must sell in order to meet the requirements, we need to consider the total cost of chairs and tables. Let's break it down:

Tables: If the store sold 10 tables for $400 each, the total cost of tables is 10 * 400 = $4000.

Minimum sales requirement: The store must sell a minimum of $6500 worth of chairs and tables. Since the cost of tables is already $4000, the remaining amount should come from the chairs. Therefore, the minimum amount of chairs to be sold is (6500 - 4000) / 150 = 20.

So, the online furniture store must sell a minimum of 20 chairs in order to meet the requirements.

Answer 2

17 chairs

Step-by-step explanation:

400t+150c\ge 6500

400t+150c≥6500

\text{Plug in }\color{green}{10}\text{ for }t\text{ and solve each inequality:}

Plug in 10 for t and solve each inequality:

The store sold 10 tables

400t+150c≥6500

400(10)+150c≥6500

4000+150c≥6500

150c≥2500

c≥16.67

​

\text{The values of }c\text{ that make BOTH inequalities true are:}

The values of c that make BOTH inequalities true are:

\{17,\ 18,\ 19,\ 20\}

{17, 18, 19, 20}

Therefore the minimum number of chairs that the store must sell is 17.