Question

A party rental company has chairs and tables for rent. The total cost to rent 9 chairs and 7 tables is $91. The total cost to rent 3 chairs and 5 tables is $59. What is the cost to rent each chair and each table? Costtorenteachchair:$ Costtorenteachtable:$

Answer 1

cost to rent each chair=$1.75, cost to rent each tabble=$10.75

Explanation:

Hello, I can help you with this

Step 1

Define

cost to rent a chair=x

cost to rent a table=y

9x=total cost for rent 9 chair

7y = total cost for rent 7 tables

a)The total cost to rent 9 chairs and 7 tables is $91.

in mathematical terms it is

9x+7y=91....equation 1

b) The total cost to rent 3 chairs and 5 tables is

3x+5y=59.... equation 2

and you have 2 equation and 2 unknown terms

let's solve this

from equation 1 isolate x

`9x+7y=91\\9x=91-7y\\x=(91-7y)/(9)\\ \\`

from equation 2 isolate x

`3x+5y=59\\3x=59-5y\\x=(59-5y)/(3)`

now, x= x, so

`x=(91-7y)/(9)\\\\\\x=(59-5y)/(3) \ \\\ (91-7y)/(9)=(59-5y)/(3)\\ 3(91-7y)=9(59-5y)\\273-21y=531-45y\\273-531=-45y+21y\\-258=-24y\\y=(258)/(24)\\ y=10.75\\`

now, we know y, use it to find x

`x=(59-5y)/(3)\\x=(59-5(10.75))/(3)\\x=(59-53.75)/(3)\\\\x=(5.25)/(3)\\ x= 1.75\\`

Have a nice day