A party rental company has chairs and tables for rent

Question

A party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 6 tables is $64

. The total cost to rent 5 chairs and 3 tables is $37 What is the cost to rent each chair and each table?

Answer 1

the problem is solvable. Leet c = cost of chairs and t = cost of tables. Then,

2c+6t=64 and 5c +3t=37. From first equation, c + 3t = 32 . sub in 2nd equation, you have

5(32-3t)+3t=37. 160 -15t+3t=37, -12t=-123, t = $10.25, the cost of a table. c = 32-3t, or 32-3(10.25)=$1.25

Answer 2

2c+6t = 64 is the 1st given equation

divide by 2 to get

c +3t = 32

5c+3t =37 is the 2nd given equation

c +3t = 32

subtract to eliminate one variable, leaving

4c = 5

c = $1.25 per chair

t= (32-c)/3= 30.75/3 = $10.25 per table

check the answers

plug c=1.25 and t=10.25 into the 2 original equations

5(1.25)+ 3(10.25)

= 6.25 + 30.75

= 37

2(1.25) + 6(10.25)

= 2.5 + 61.5

= 64

solve by substitution, elimination, matrix (linear) algebra or graphing