Solving a word problem using a system of linear equations of the form Ax + By = C

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?

Cost to rent each chair?

Cost to rent each table?

Answer 1

Let cost to rent each chair be represented by variable "c"

Let cost to rent each table be represented by variable "t"

Given : 2c + 6t = 64

& 5c + 3t = 37

2 equations and 2 unknowns., To solve them as per requirement as follows:

Multiply second equation by 2, we have 10c + 6t = 74

and write down both again and subtract 2nd from 1st

2c +6t =64

-(10c +6t = 74) = > -8c = -10, c = -10/-8 = 10/8 = 1.25

t could be solved the similar way or by substitution

Using substitution:

2(1.25)+6t=64 or 6t = 64 - 2(1.25) => 6t =64-2.5 => 6t =61.5

t = 61.5/6 = 10.25

Hence, cost to rent each chair =$1.25

cost to rent each table = $10.25

Answer 2

2c + 6t = 64 (1)

5c + 3t = 37 (2)

10c + 6t = 74 2 (2)

8c = 10 2(2) - (1)

c = 10/8 = $ 1.25

6t = 64 - 2c = 61.5

t = 61.5 / 6 = $ 10.25

5 chairs and 3 tables, 5 x 1.25 + 3 x 10.25 = 37