Question

a party rental company has chairs and tables to rent. there were two customers who rented both chairs and tables last week. the table below shows the number of chairs, the number of tables, and the total cost (in dollars) for those two customers.
first customer
second customer
number of chairs
3
9
number of tables
5
7
total cost (in dollars)
52
86
let x be the cost (in dollars) to rent a chair.
let y be the cost (in dollars) to rent a table.
(a) write a system of equations that could be used to find the rental cost (in dollars) of each chair and each table.
$\square x + \square y = \square$
$\square x + \square y = \square$
(b) how much does each chair and each table cost (in dollars) to rent?
cost to rent each chair: $\square$
cost to rent each table: $\square$

Explanation:

Step1: Set up first customer's equation

The first customer rented 3 chairs and 5 tables for $52, so:
$3x + 5y = 52$

Step2: Set up second customer's equation

The second customer rented 9 chairs and 7 tables for $86, so:
$9x + 7y = 86$

Step3: Eliminate x variable

Multiply the first equation by 3:
$3(3x + 5y) = 3(52)$
$9x + 15y = 156$
Subtract the second equation from this new equation:
$(9x + 15y) - (9x + 7y) = 156 - 86$
$8y = 70$

Step4: Solve for y

Calculate the value of y:
$y = \frac{70}{8} = 8.75$

Step5: Substitute y to find x

Plug $y=8.75$ into $3x + 5y = 52$:
$3x + 5(8.75) = 52$
$3x + 43.75 = 52$
$3x = 52 - 43.75$
$3x = 8.25$
$x = \frac{8.25}{3} = 2.75$

Answer:

(a) System of equations:

$3x + 5y = 52$
$9x + 7y = 86$

(b)

Cost to rent each chair: $\$2.75$
Cost to rent each table: $\$8.75$