Garrett and Judy Kay are considering buying a new fridge to replace their older one.
Step 2: Identify Variables and Assumptions
They estimate that their current (older) fridge, which they got for free, costs them about $16 a month in electricity charges to operate. They found a new fridge that costs $1,150 to purchase and would cost only around $5 a month in electricity charges.
The new fridge comes with a 10-year warranty, so they assume the new fridge to last for 10 years without any extra repair or replacement fees.
If they keep their old fridge, then they assume they will need to pay around $250 sometime over the next 10 years in maintenance costs to keep it running.
(For this comparison, assume they set aside the money to maintain the old fridge right at the beginning of the 10 years, even though they probably won't need the money until several years later.)
Let x represent the number of months. Let y represent total cost in dollars.
Step 3: Apply Quantitative Tools
Set up a system of equations that could be used to help Garrett and Judy Kay decide if buying the new fridge is worth it.
Create functions that describe the total cost in dollars for each fridge.
New Fridge Total Cost Function
y= 5x+1150
Old Fridge Total Cost Function
y= 16x+250
Use your functions to calculate the total cost for each fridge after 6 months.
New Fridge:
1180
(Round to the nearest whole dollar)
Old Fridge:
346
(Round to the nearest whole dollar)
Use your functions to calculate the total cost for each fridge after 10 years. (Hint: your function is set for months so you will have to convert years to months)
New Fridge:
1750
(Round to the nearest whole dollar)
Old Fridge:
2170
(Round to the nearest whole dollar)
At how many months is the total cost for each fridge the same?
Number
(Round to one decimal place)
How many years is this?
Number
(Round to one decimal place)
True or False: Before this time, the new fridge total cost is more than the old fridge.
True*
False
True or False: After this time, the new fridge total cost is more than the old fridge.
True
False*
Step 4: Make an Informed Decision
What would you advise Garrett and Judy Kay to do?
Option #1: Buy a new fridge
Option #2: Keep the old fridge
Option #
2
Step 5: Evaluate Your Reasoning
In your opinion, is the new fridge a good decision that will save them money in the long run?
