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

Question

One month Amy rented 8

 movies and 4

 video games for a total of $45

. The next month she rented 3

 movies and 2

 video games for a total of $20

. Find the rental cost for each movie and each video game.

Answer 1

Ax + By = C

is the format for the equations:

8x + 4y = 45

3x + 2y = 20

where x is the rental cost per movie and y is the rental cost per video game.

One method of solving these equations is variable elimination. Multiply the second equation by 2:

6x + 4y = 40

Subtract it fron the first equation:

2x= 5

NOTE that y was eliminated from this equation.

Divide both sides by 2:

x = 2.5

Substitute this value for x back in the first equation and solve for y:

8(2.5) + 4y = 45

20 + 4y = 45

Subtract 20 from both sides:

4y = 25

Divide both sides by 4:

y = 6.25

Check these x and y values in the second equation:

3(2.5) + 2(6.25) = 7.5 + 12.50 = 20

So we have found and verified the solution to our equations:

The rental cost per movie is $2.50 and the rental cost per video game is $6.25.