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 5 chairs and 3 tables is $35. The total cost to rent 7 chairs and 9 tables is $91. 

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

Answer 1

Let X = number of chairs and Y = number of table

So

5X + 3Y = $35

and

7X + 9Y = $91

Solve bottom equation for Y

9Y = 91 - 7X

Y = (91 -7X ) / 9

Y = 10.11 - .778 X

Substitute this Y value into first equation - then solve for X

5X + 3( 10.11 -.778 X) = $35

5X + 30.33 - 2.334 X = $35

2.666 X = 35 - 30.33

2.666 X = 4.67

X = $1.75 cost per chair

Sub cost of a chair into either equation to find Y cost of a Table

5X + 3Y = $35

5 (1.75) + 3 Y = $35

8.75 + 3Y = 35

3Y = 35 - 8.75

Y = 26.25 / 3

Y = $8.75

Check - Substitute values into both equations

Answer 2

5C+3T = 35

7C +9T=91

multiply 1st equation by 3 and then subtract from that the 2nd equation

15C+9T = 105

7C +9T = 91

______________

8C = 14

C = 14/8 = 7/4 = $1.75

3T =35-5(7/4) = 35-35/4 =3(35)/4 = 105/4 = $26.25

T = 26.25/3= $8.75

tables cost $8.75, chairs $1.75

Answer 3

Create variables to represent the chairs and the tables.

5x + 3y = 35

7x + 9y = 91

multiply the first equation by -3 then add the two together. The reason you are doing this is to cancel out the y variable and solve for x.

-15x - 9y = -105

7x + 9y = 91

Now use this to solve for x

-8x = -14

x = 1.75

Plug this into the equation and solve for y.

7x + 9y = 91

12.25 + 9y = 91

9y = 78.75

y = 8.75

Cost of each chair: $1.75

Cost of each table : $8.75