The total cost to rent 8 chairs and 4 tables is $45. The total cost to rent 3 chairs and 2 tables is $21. What is the cost to rent each chair and each table?

Answer 1

Hi Chantelle, the way to answer this question is to turn each statement into an algebraic equation. The two unknowns are:

cost of the chair (which we will label "x") and

cost of the table (which we will label "y").

So, we know that 8x (8 chairs) + 4y (4 tables) = $45

We also know that 3x (3 chairs) + 2y (2 tables) = $21

We need to solve for either x or y, and one good way of doing this is to multiply/divide one of the equations by some number that will allow us to combine them in such a way that either "x" or "y" will cancel out, leaving us with just one variable. In this case, if we multiply the 2nd equation by 2, then we will have 4y in both equations and we can subtract the 2nd equation from the 1st in order to just have "x".

2nd equation x 2 = (3x+2y = 21) x 2 = 6x + 4y = $42.

Now if we subtract this new equation from the 1st equation:

8x + 4y = 45

- (6x + 4y = 42)

= (2x = 3)

3/2 = $1.50. So x (cost of renting a chair) is equal to $1.50. Now that we've solved for x, simply plug this value in to either equation instead of "x" and solve for y! Hope this helps :)