Answer:
A chair costs $2.50 each and a table costs $6 each.
Step by Step Explanation:
First, let's break this down to two equations.
Equation 1: 2c + 5t = 35
Equation 2: 8c + 5t = 38
Let's first solve for "t" (tables) by modifying Equation 1 so that it has the same number of chairs as Equation 2.
To do that, we must times the equation by 4, so:
4(2c + 5t = 35) -> 8c + 20t = 140.
So now the two equations we have are:
1: 8c + 20t = 140
2: 8c + 3t = 38
Now that they have the same number of chairs (8c), we can subtract Equation 2 from Equation 1, and that gets us the following:
17t = 102
t = 102 / 7 = 6.
Therefore, a table costs $6.00 to rent.
Knowing this, we can use either equation to now find "c". Let's use Equation 1.
2c + 5(6) = 35
2c + 30 = 35
2c = 5
c = 5 / 2 = 2.5
So now we know each chair costs $2.50 to rent. Let's use Equation 2 to confirm both the costs of the table and the chair.
8(2.5) + 3(6) = 38
20 + 18 = 38
38 = 38.
Therefore, each chair costs $2.50 and each table costs $6.
