Question

The total cost to rent 3 chairs and 2 tables is $17 . The total cost to rent 8 chairs and 4 tables is $37 . What is the cost to rent each chair and each table?

Answer 1

Let's make some variables to represent the cost of the tables and chairs.

Let x be equal to the cost of one chair
Let y be equal to the cost of one table

The total cost for 3 chairs and 2 tables is $17.

3x + 2y = 17

The total cost for 8 chairs and 4 tables is $37.

8x + 4y = 37

Now we have our system of equations.
Let's solve it.

3x + 2y = 17
8x + 4y = 37

We can cancel the y's very easily. Then it would just leave us with the x's.
Multiply the top equation by -2.

3x(-2) + 2y(-2) = 17(-2) = 
-6x - 4y =  -34

Then add the equations together.

-6x - 4y = -34
8x + 4y = 37
        =
2x = 3

Then just divide both sides by 2.

x = 1.5

Substitute 1.5 into one of the equation. I'll pick 3x + 2y = 17

3(1.5) + 2y = 17 ; Start
4.5 + 2y = 17      ; Multiply 3 and 1.5 together
2y = 12.5             ; Subtract 4.5 from each side of the equation
y = 6.25                ; Divide both sides by the coefficient of y. Which 2

So, a chair costs $1.50 and a table costs $6.25. 

Answer 2

3+2 = 5
8 + 4  = 12 
37 / 12 = 3.08
5 / 17  = 3 .04 
so i would say 3 dollars