O Graphs, Functions, and Systems
Solving a word problem using a system of linear equations of the form Ax...
Erin
A party rental company has chairs and tables for rent. The total cost to rent 8 chairs and 3 tables is $\$ 36$. The total cost to rent 2 chairs and 5 tables is $\$ 43$. What is the cost to rent each chair and each table?
Cost to rent each chair: $s \square$
Cost to rent each table: $s \square$

Step 1 ：Let's denote the cost to rent each chair as \(x\) and the cost to rent each table as \(y\).

Step 2 ：From the problem, we can form two equations: \(8x + 3y = 36\) and \(2x + 5y = 43\).

Step 3 ：First, let's multiply the first equation by 2 and the second equation by 8 to make the coefficients of \(x\) the same in both equations: \(16x + 6y = 72\) and \(16x + 40y = 344\).

Step 4 ：Now, subtract the first equation from the second: \(34y = 272\).

Step 5 ：Divide both sides by 34 to solve for \(y\): \(y = 272 / 34 = 8\).

Step 6 ：Now that we have \(y\), we can substitute it into the first equation to solve for \(x\): \(8x + 3*8 = 36\), \(8x + 24 = 36\), \(8x = 36 - 24\), \(8x = 12\), \(x = 12 / 8 = 1.5\).

Step 7 ：So, the cost to rent each chair (\(x\)) is \(\boxed{1.5}\) and the cost to rent each table (\(y\)) is \(\boxed{8}\).

Step 8 ：Let's check our solution: \(8*1.5 + 3*8 = 12 + 24 = 36\) and \(2*1.5 + 5*8 = 3 + 40 = 43\). Both equations are true, so our solution is correct.