Question

A party rental company has chairs and tables for rent. The total cost to rent 3 chairs and 5 tables is $39 . The total cost to rent 9 chairs and 7 tables is $63 .

What is the cost to rent each chair and each table?

Answer 1

• chair: $1.75
• table: $6.75

Explanation:

If we let c and t represent the rental costs of a chair and a table, respectively, the problem statement tells us ...

• 3c +5t = 39
• 9c +7t = 63

These equations can be solved numerous ways. My favorite for something like this is to use the matrix functions of my calculator. Another useful method is provided by Cramer's rule. It tells us the solution to ...

• ax +by = c
• dx +ey = f

is given by ...

• ∆ = bd -ea
• x = (bf -ec)/∆
• y = (cd -fa)/∆

Putting the numbers from our given equations into these formulas, we get ...

• ∆ = 5·9 -7·3 = 24
• c = (5·63 -7·39)/24 = 42/24 = 1.75
• t = (39·9 -63·3)/24 = 162/24 = 6.75

The cost to rent each chair is $1.75; the cost to rent each table is $6.75.