Question

a party rental company has chairs and tables for rent the total cost to rent three chairs and eight tables is $58 the total cost to rent 5 chairs and two tables is $23 what is the cost to rent each chair in East table

Answer 1

Let 'c' be the cost to rent one chair and let 't' be the cost to rent one table.

Then, since three chairs and eight tables cost $58, then:

`3c+8t=58`

also, the cost to rent 5 chairs and two tables is $23,then:

`5c+2t=23`

we have the following system of equations:

`\begin{cases}3c+8t=58 \\ 5c+2t=23\end{cases}`

now, if we multiply by -4 the second equation, we get:

`\begin{gathered} -4\cdot(5c+2t=23) \\ \Rightarrow-20c-8t=-92 \end{gathered}`

then, if we add this equation with thte first equation from the system, we get the following:

`\begin{gathered} 3c+8t=58 \\ -20c-8t=-92 \\ ----------- \\ -17c=-34 \\ \Rightarrow c=(-34)/(-17)=2 \\ c=2 \end{gathered}`

now that we have that c = 2, we can use this value to find the cost of the tables with the first equation:

`\begin{gathered} 3(2)+8t=58 \\ \Rightarrow6+8t=58 \\ \Rightarrow8t=58-6=52 \\ \Rightarrow t=(52)/(8)=6.5 \\ t=6.5 \end{gathered}`

therefore, the cost to rent each chair is $2 and the cost to rent each chair is $6.5