Question

A party rental company has chairs and tables for rent .the total cost to rent 8 chairs and 4 tables is $53 the total cost to rent 3 chairs and 2 tables is $24 what is the cost to rent a chair and each table

Answer 1

To determine the cost to rent a chair and each table, we solve the system of linear equations derived from the given total costs. By calculation, the cost to rent a chair is $2.50 and the cost to rent a table is $8.25.

Step-by-step explanation:

The question involves solving a system of linear equations to find the cost to rent each chair and each table from a party rental company.

We can represent the cost of a chair as 'c' and the cost of a table as 't'. The first equation based on the given information is:
8c + 4t = $53 (1)

The second equation would be:
3c + 2t = $24 (2)

By solving these two equations simultaneously, we can find the individual costs of a chair and a table.

Start by multiplying Equation (2) by 2 for easier elimination: 6c + 4t = $48.

Now subtract the new equation from Equation (1): (8c + 4t) - (6c + 4t) = ($53 - $48) which simplifies to 2c = $5.

Divide both sides by 2 to find the cost of one chair: c = $2.50.

Insert the value of c into Equation (2) to find t: 3(2.50) + 2t = $24, which simplifies to 7.50 + 2t = $24.

Subtract 7.50 from both sides to solve for t: 2t = $16.50.

Lastly, divide by 2 to get the cost of one table: t = $8.25.

Therefore, the cost to rent a chair is $2.50, and the cost to rent a table is $8.25.

Answer 2

In order to solve this problem, we will let be
c= chairs, t=tables and have the following equations
8c+4t=53
3c+2t=24
we can solve this system by multiplying the second equation with -2 and add it to the first one
8c+4t=53
-6c-4t=-48
we add them and get
2c=5, therefore c=5/2=2.5 , so to rent a chair you need to pay 2.50 dollars
now we will replace c with 2.50
3*(2.50)+2t=24
7.50+2t=24 subtract 7.50 from both sides
2t=24-7.50
2t=16.50
t=16.50/2=8.25 8.25 to rent a table

we want to verify our answer
8(2.50)+4(8.25)=20+33=53
correct!!!!!