Individual Service
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So you ask: when do we use systems of equations in everyday life?? Well, to be honest, most likely you will
not use the exact math that you learn in class in your day-to-day life. However, the problem solving skills that you
acquire when learning how to solve a system of equations will help you when you are presented with a decision
that will require you to determine what your best option would be.
Here are a couple of examples of ways you will use this type of problem solving in your everyday life:
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Buying a car with a monthly payment
Choosing a type of car insurance
Deciding what house/apartment to buy or rent
Choosing your right type of health insurance
Buying a cell phone plan
In the following scenario, Alice has decided to switch her cell phone plan to T-Mobile. She originally had Cricket
and they only had one price per month for unlimited minutes, so she is having a hard time deciding what the best
plan would be; she needs your help!
Our friend Alice has looked at all of her options online and decides that she talks a fair amount, but not too much.
She wants to know what kind of deal she is getting if she buys the myFaves1500 plan vs. the myFaves300 plan.
However, T-Mobil is offering a great deal if you buy the plan with more minutes: you get $70 off of a new phone!
 myFaves300 plan = $100 for a new cell phone with the service
 myFaves1500 plan = $30 for a new cell phone with the service
Use the above information and the service plan information given to you below to answer the following questions
and help decide which cell phone plan will give Alice the better deal.
Plan name
Whenever Minutes Weekend/ Night Mins
myFaves Minutes
Price per month
Our Most Popular Plan
myFaves 300
300
Unlimited
Unlimited
$40.00
myFaves 1500
1500
Unlimited
Unlimited
$70.00
Step 1: Create two equations – one that models the cost of each cell phone plan (use x and
y as your variables)
a. Define your variables:
x: ________________________________ y: _________________________________
b. Write one equation for each cell phone plan (with a new cell phone):
Equation 1: ________________________________
Equation 2: ________________________________
Step 2: Make sure your equation is in y = mx + b form and graph your system of equations
on the same axis.
a. Estimate the solution using your graph: _____________________
Step 3: Use substitution to find the exact solution to the system of equations (Remember:
what do the two variables represent in your equations).
Use your graph and the solution you found to answer the following questions:
a. After how many months will the two plans cost exactly the same?
b. How much will they both cost when they are at the same price?
c. If she plans on signing a year-long contract and she won’t use very many minutes per
month, what is the best plan for Alice to buy. Explain your reasoning.
d. Why do you think cell phone companies make it so cheap to buy a new cell phone with
the plans that cost more money per month?