Question

Consider two situations: Situation 1: In Lakeville, Melinda’s television cable bill is a flat rate of $50 per month, plus $1.50 for every movie she rents. After one month of service, her bill is $66.25. Situation 2: In Oceanside, Kimberly’s television cable bill is a flat rate of $60 dollars per month, plus $1.25 for every movie she rents. If you were to model these two situations with equations to solve for all the unknowns, what similarities and differences would the equations have? Can you solve for all the unknowns in both situations?

Answer 1

situation 1 : flat rate of 50....1.50 per movie.....after 1 month her bill is 66.25
66.25 = 1.50x + 50

situation 2 : flat rate of 60....1.25 for every movie...
y = 1.25x + 60

both situations have a flat rate fee plus a charge for every movie. In situation 1, u can solve for x (the number of movies rented) because u know how much she was charged. However, in situation 2, without more information, u cannot solve this equation...what u would need to solve it would either be the number of movies rented or the total bill showing what she was charged. So basically, in situation 1, u are given more information then in situation 2.....enough information to be able to solve for the variable x...whereas, in situation 2, u are not given enough info to solve for a variable and get a numerical answer

Answer 2

The difference is it is easy to find the value of unknowns variable of situation 1 while difficult for situation 2. In situation 2 we can not solve for all the unknowns, while it is possible to solve all the unknowns for Situation 1.

Explanation:

Consider the provided information.

Situation 1: In Lakeville, Melinda’s television cable bill is a flat rate of $50 per month, plus $1.50 for every movie she rents. After one month of service, her bill is $66.25.

The flat rate is 50, means 50 is the fixed charge and for every movie you needs to pay 1.50 where the total bill is 66.2

This information can be written as:

66.25 = 1.50x + 50

Now consider the second situation: In Oceanside, Kimberly’s television cable bill is a flat rate of $60 dollars per month, plus $1.25 for every movie she rents.

Flat rate is 60 means 60 is the fixed charge and for every movie you needs to pay 1.25. Let the total bill is y then the equation can be written as:

y = 1.25x + 60

In situation 1 it is easy to find the value of unknowns variable.

Thus, the difference is it is easy to find the value of unknowns variable of situation 1 while difficult for situation 2.

In situation 2 we can not solve for all the unknowns, while it is possible to solve all the unknowns for Situation 1.