Given:
a. The total cost to rent 5 chairs and 3 tables is $27.
b. The total cost to rent 2 chairs and 12 tables is 81 dollars.
To be able to determine the cost of the rent of each chair and table, let's convert the following given into a mathematical expression and determine the solution by Substitution Method.
Let,
x = rental cost of each chair
y = rental cost of each table
We get,
a. The total cost to rent 5 chairs and 3 tables is $27: 5x + 3y = 27
b. The total cost to rent 2 chairs and 12 tables is 81 dollars: 2x + 12y = 81
5x + 3y = 27
3y = 27 - 5x
3y/3 = (27 - 5x)/3
y = (27 - 5x)/3
Substitute y = (27 - 5x)/3 in 2x + 12y = 81.
2x + 12y = 81
2x + 12[(27 - 5x)/3] = 81
2x + 4(27 - 5x) = 81
2x + 108 - 20x = 81
2x - 20x = 81 - 108
-18x = -27
-18x/-18 = -27/-18
x = 27/18
x = $1.50
Therefore, the rental cost of the chair is $1.50.
Let's now determine the rental cost of each table. Substitute x = 1.50 in 5x + 3y = 27.
5x + 3y = 27
5(1.5) + 3y = 27
7.5 + 3y = 27
3y = 27 - 7.5
3y = 19.5
3y/3 = 19.5/3
y = $6.50
Therefore, the rental cost of each table is $6.50.
In summary,
Therefore, the rental cost of the chair is $1.50
Therefore, the rental cost of each table is $6.50