Question

A party rental company has chairs and tables for rent. The total cost to rent 5

chairs and 3
tables is $35
. The total cost to rent 7
chairs and 9
tables is $91
. What is the cost to rent each chair and each table?

Answer 1

let chairs be
`c` and table be
`t`
We form two equations from the information given so we can solve simultaneously

Eq 1 ⇒
`5c+3t=35`
Eq 2 ⇒
`7c+9t=91`

We can either use the method of elimination or substitution. We will use the elimination method for this one

Let us eliminate the term
`c`. We need to make the two constants the same. We have
`5c` and
`7c` and we can make them both as
`35c`.

We will multiply each term in Eq 1 by 7 to obtain
`35c+21t=245`

We will multiply each term in Eq 2 by 5 to obtain
`35c+45t=455`

Now we subtract Eq 2 from Eq 1 to obtain

`(35c-35c)+(21t-45t)=(245-455)`

`-24t=-210`

`t= (210)/(24)=8.75`

So the price of one table is $8.75

Substitute 8.75 into either Eq 1 or Eq 2 to obtain the price for one chair. Let's use Eq 1


`5c+3(8.75)=35`

`5c+26.25=35`

`5c=35-26.25`

`5c=8.75`

`c=1.75`

So the price of one chair is $1.75