On the homedepot.com website, a General Electric 40-gallon electric hot water tank retails for $218 and the estimated annual cost of operation is $508. Write an expression for the cost to buy and run the hot water tank for x years.
The Correct Answer and Explanation is :
To express the total cost of buying and running the hot water tank for ( x ) years, we can break it down into two parts: the cost of buying the tank and the cost of operating it.
Cost of Buying the Tank:
The cost to purchase the tank is a one-time expense of $218.
Cost of Operating the Tank:
The estimated annual operating cost is $508 per year. For ( x ) years, the total operating cost would be the annual cost multiplied by the number of years, so it’s ( 508x ).
Expression for the Total Cost:
To find the total cost of buying and running the hot water tank for ( x ) years, we add the one-time cost of the tank to the operating cost over ( x ) years:
[
\text{Total Cost} = 218 + 508x
]
Explanation:
- The $218 represents the upfront cost of purchasing the General Electric 40-gallon electric hot water tank.
- The $508 represents the estimated annual cost to operate the tank, which includes electricity and maintenance.
- ( x ) is the number of years you plan to own and use the tank.
- The expression ( 508x ) gives the total operating cost for ( x ) years.
- By adding $218 to ( 508x ), we account for both the purchase price and the operating costs.
For example, if you were to use the tank for 5 years, the total cost would be:
[
\text{Total Cost} = 218 + 508(5) = 218 + 2540 = 2758
]
So, after 5 years, the total cost would be $2,758.
This expression gives you a way to calculate the overall cost based on how long you plan to use the hot water tank. The formula is linear because both the purchase price and operating costs are constant, and the total cost increases directly with the number of years you use the tank.