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.

9

Step-by-step explanation:

\underline{\text{Define Variables:}}

Define Variables:

May choose any letters.

\text{Let }t=

Let t=

\,\,\text{the number of tables sold}

the number of tables sold

\text{Let }c=

Let c=

\,\,\text{the number of chairs sold}

the number of chairs sold

\text{\textquotedblleft a maximum of 20 pieces"}\rightarrow \text{20 or fewer pieces}

“a maximum of 20 pieces"→20 or fewer pieces

Use a \le≤ symbol

Therefore the total number of furniture pieces sold, t+ct+c, must be less than or equal to 20:20:

t+c\le 20

t+c≤20

\text{\textquotedblleft at least \$5000"}\rightarrow \text{\$5000 or more}

“at least $5000"→$5000 or more

Use a \ge≥ symbol

The store makes $550 for each table sold, so for tt tables, the store will make 550t550t dollars. The store makes $50 for each chair sold, so for cc chairs, the store will make 50c50c dollars. Therefore, the total revenue 550t+50c550t+50c must be greater than or equal to \$5000:$5000:

550t+50c\ge 5000

550t+50c≥5000

\text{Plug in }9\text{ for }c\text{ and solve each inequality:}

Plug in 9 for c and solve each inequality:

The store sold 9 chairs

\begin{aligned}t+c\le 20\hspace{10px}\text{and}\hspace{10px}&550t+50c\ge 5000 \\ t+\color{green}{9}\le 20\hspace{10px}\text{and}\hspace{10px}&550t+50\left(\color{green}{9}\right)\ge 5000 \\ t\le 11\hspace{10px}\text{and}\hspace{10px}&550t+450\ge 5000 \\ \hspace{10px}&550t\ge 4550 \\ \hspace{10px}&t\ge 8.27 \\ \end{aligned}

t+c≤20and

t+9≤20and

t≤11and

550t+50c≥5000

550t+50(9)≥5000

550t+450≥5000

550t≥4550

t≥8.27

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

The values of t that make BOTH inequalities true are:

\{9,\ 10,\ 11\}

{9, 10, 11}

Therefore the minimum number of tables that the store must sell is 9.

the answers c

step-by-step explanation:

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