A party rental company has chairs and tables for rent

Question

The total cost to rent 8 chairs and 3 tables is $42. The total cost to rent 2 chairs and 5 tables is $53. What is the cost to rent each chair and each table ?

Answer 1

Let C= Cost per chair

Let T = Cost per table

The total cost to rent 8 chairs and 3 tables is $42.

8C+3T=42

The total cost to rent 2 chairs and 5 tables is $53.

2C+5T=53

What is the cost to rent each chair and each table ?

First step is to solve for one variable.

Lets Solve for C

2C+5T=53

-5T -5T

2C=53-5T

/2 2

C=53-5T

2

Now substitute for C in the other equation

8C+3T=42

8(53-5T) +3T=42

2

(424-40T) +3T= 42

2

212-20T+3T=42

-212 -212

-17T=-170

/-17 /-17

T=10

C=53-5T

2

C= 53-5(10)

2

C=3/2

C=1.5

Check

8C+3T=42

8(1.5)+3(10)=42

12+30=42

Answer 2

c=cost of one chair rental

t=cost of one table rental

8c+3t=42

2c+5t=53

multiply the second equation,each term on both sides, by -4

8c+3t=42

-8c-20t=-212

add the two equations

-17t=-170

divide both sides by -17

t=$10 to rent one table

substitute t=10 into either original equation

2c+5(10)=53

2c+50=53

2c=3

c=$1.50 to rent one chair

Answer 3