Question

A party rental company has a chair and tables for rent.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 ?cost to rent each chair cost to rent each table

Answer 1

if x is the cost of one chair and y is the cost of one table, then, you have the following system:

3x + 2y = 17

8x + 4y = 37

in order to solve the previous system of equations, multiply the first equation by 8 and the second equation by 3, and the subtract them, as follow:

(3x + 2y = 17)(8)

24x + 16y = 136

(8x + 4y = 37)(3)

24x + 12y = 111

24x + 16y = 136

-24x - 12y = -111

4y = 25

solve for y:

y = 25/4

next, replace the previous value of y into the first equation and solve for x:

3x + 2(25/4) = 17

3x + 25/2 = 17

3x = 17 - 25/2

3x = (34 - 25)/2

3x = 9/2

x = 9/6

x = 3/2

Hence, the cost of one chair and one table is:

one table = 25/4 = $6.25

one chair = 3/2 = $1.5