A party rental company has chairs and tables for rent. The total cost to rent 5 chairs and 3 tables is $41. The total cost to rent 7 chairs and 9 tables is $109. What is the cost to rent each chair and each table?

Due by midnight

Chair = $1.75

Table = $10.75

Step-by-step explanation:

Let the cost of renting each chair be A and that of table be B

Given cost to rent 5 chairs and 3 tables is $41

That’s

5A + 3B = 41

Also, the cost of renting 7 chairs and 9 tables is $109

That’s

7A + 9B = 109

We no have two equations

1. 5A + 3B = 41

2. 7A + 9B = 109

Multiply equation 1 by 7 answers equation 2 by 5 so we can eliminate A

We have

7 x 5A + 7 x 3B = 7 x 41

5 x 7A + 5 x 9B = 5 x 109

35A + 21B = 287

35A + 45B = 545

Subtract equation 2 from equation 1

-24B = -258

Divide both sides by -24

-24B/-24 = -258/-24

B = $10.75

Now substitute 10.75 for B in either equations to get A.

Using equation 1, we have

5A + 3B = 41

5A + 3 x 10.75 = 41

5A + 32.25 = 41

Subtract 32.25 from both sides

5A + 32.25 - 32.25 =41-32.25

5A = 8.75

Divide both sides by 5 to get A

5A/5 = 8.75/5

A = $1.75

Each chair cost $1.75 and each table cost $10.75

Check

5(1.75) + 3(10.75) = 41