Answer:
4 tables
Step-by-step explanation:
14 chairs = $1400
3900 - 1400 = 2500
3 tables = $2100 with a remainder of 400
you need to add 1 more table so it meets the minimum so the answer is 4 tables
Answer:
9
Step-by-step explanation:
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 at most 21 pieces"}\rightarrow \text{21 or fewer pieces}
“at most 21 pieces"→21 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 21:21:
t+c\le 21
t+c≤21
\text{\textquotedblleft no less than \$5700"}\rightarrow \text{\$5700 or more}
“no less than $5700"→$5700 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 $100 for each chair sold, so for cc chairs, the store will make 100c100c dollars. Therefore, the total revenue 550t+100c550t+100c must be greater than or equal to \$5700:$5700:
550t+100c\ge 5700
550t+100c≥5700
\text{Plug in }10\text{ for }c\text{ and solve each inequality:}
Plug in 10 for c and solve each inequality:
The store sold 10 chairs
\begin{aligned}t+c\le 21\hspace{10px}\text{and}\hspace{10px}&550t+100c\ge 5700 \\ t+\color{green}{10}\le 21\hspace{10px}\text{and}\hspace{10px}&550t+100\left(\color{green}{10}\right)\ge 5700 \\ t\le 11\hspace{10px}\text{and}\hspace{10px}&550t+1000\ge 5700 \\ \hspace{10px}&550t\ge 4700 \\ \hspace{10px}&t\ge 8.55 \\ \end{aligned}
t+c≤21and
t+10≤21and
t≤11and
550t+100c≥5700
550t+100(10)≥5700
550t+1000≥5700
550t≥4700
t≥8.55
\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.
