An online furniture store sells chairs for $50 each and tables for $550 each. Every day, the store can ship a maximum of 20 pieces of furniture and must sell at least $5000 worth of chairs and tables. If 9 chairs were sold, determine the minimum number of tables that the the store must sell in order to meet the requirements. If there are no possible solutions, submit an empty answer.

If 9 chairs were sold, the store must sell 11 tables in order to meet the requirements.

Step-by-step explanation:

Selling price of each table = $50

Selling price of each table = $550

Let the number of chairs sold in a a day = x

Let Number of tables old in a a day = y

Hence, the selling price of x chairs = x times $50 = 50 x

and the selling price of y tables = y times $550 = 550 y

Maximum number of pieces that can be shipped = 20

⇒ x + y ≤ 20

Also, The total selling amount should at least be $5,000

⇒ 50 x + 550 y ≥ 5,000

Hence, the given system of equation is:

x + y ≤ 20

50 x + 550 y ≥ 5,000

Solving the given system:

put y = 20 - x from (1) in the equation (2), we get

50 x + 550 y = 5,000 ⇒ 50x + 550 (20 - x) = 5000

or, 50x + 11,000 - 550x = 5000

or, - 500x = - 6000

x = 12

or the number of chairs sold at maximum = 12

also, y = 20 - x = 20 - 12 = 8

So, number of tables sold at maximum = 8

Now, if the number of chairs sold = 9,

then the number of tables sold = 20 - 9 = 11

The selling amount is 50 (9) + 550 (11) = $6,500 > $5,000

Hence, 9 chairs were sold, the store must sell 11 tables in order to meet the requirements.