A party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 5 tables is $35. The total cost to rent 8 chairs and 3 tables is $38.00. What is the cost to rent each chair and each table?

Answer: The cost of renting a chair is $2.5 while the cost of renting a table is $6

Step-by-step explanation: Let the cost chair rental be called h, while the cost of table rental shall be called t. To rent two chairs and five tables cost $35, so we can express this as

2h + 5t = 35

Also to rent eight chairs and three tables cost $38, and this too can be expressed as

8h + 3t = 38

We now have a pair of simultaneous equations as follows

2h + 5t = 35 - - - (1)

8h + 3t = 38 - - - (2)

We shall use the elimination method since all the unknown variables have coefficients greater than 1.

Multiply equation (1) by 8 and multiply equation (2) by 2. We now have

16h + 40t = 280 - - - (3)

16h + 6t = 76 - - - (4)

Subtract equation (4) from (3)

34t = 204

Divide both sides of the equation by 34

t = 6

Having calculated that, substitute for the value of t into equation (1)

2h + 5 (6) = 35

2h + 30 = 35

Subtract 30 from both sides of the equation 2h = 5

Divide both sides of the equation by 2

h = 5/2 or (2.5)

Therefore the cost of rental for each chair (h) is $2.5 and the cost of rental for each table (t) is $6