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

Answer:

minimum of 13 chairs must be sold to reach a target of $6500

and a max of 20 chairs can be solved.

Step-by-step explanation:

Given that:

Price of chair = $150

Price of table = $400

Let the number of chairs be denoted by c and tables by t,

According to given condition:

t + c = 30 ----------- eq1

t(150) + c(400) = 6500 ------ eq2

Given that:

10 tables were sold so:

t = 10

Putting in eq1

c = 20 (max)

As the minimum target is $6500 so from eq2

10(150) + 400c = 6500

400c = 6500 - 1500

400c = 5000

c = 5000/400

c = 12.5

by rounding off

c = 13

So a minimum of 13 chairs must be sold to reach a target of $6500

i hope it will help you!

Answer 2

Answer:

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.