Hybrid cars can help reduce the amount of gas that a person purchases, but the technology usually makes the car have a larger up-front cost. If a person buys a hybrid car and uses it for a long period of time, they might save money. If that up-front cost is too high, though, a person might not save money.
Below is a calculation to help estimate the savings in gas to determine whether a hybrid vehicle will save money over time.
A person is purchasing a car. They are considering a hybrid car or a regular gas engine. They want to consider the cost of gas in their purchase. They expect to drive the car for \(140,000\) miles before it breaks down or they decide to sell it.
The hybrid car costs $40,000 and gets 35 miles per gallon.
The regular gas-only car costs $30,000 and gets 20 miles per gallon.
Which car will be cheaper over \(140,000\) miles? Assume gas is $4 per gallon.
The number of gallons of gas for the hybrid car is
\[140,000 \text{ miles} \div \frac{35 \text{ miles}}{\text{1 gallon}} =\]
\[140,000 \text{ miles} \cdot \frac{\text{1 gallon}}{35 \text{ miles}} =\]
\[\frac{140,000}{35} \text{ gallons} =\]
\[4,000 \text{ gallons}\]
The number of gallons of gas for the gas-only car is
\[140,000 \text{ miles} \div \frac{20 \text{ miles}}{\text{1 gallon}} =\]
\[140,000 \text{ miles} \cdot \frac{\text{1 gallon}}{20 \text{ miles}} =\]
\[\frac{140,000}{20} \text{ gallons} =\]
\[7,000 \text{ gallons}\]
The hybrid would save approximately \(3,000\) gallons. At $4 per gallon, that is a savings of \(\$4 \cdot 3,000 = \$ 12,000\).
The total cost of the traditional car, added to the extra cost in gas, is \(\$30,000 + \$12,000 = \$ 42,000\) for the regular gas car (including the cost for the extra gas). Without taking other costs into consideration, the hybrid car would save approximately \(\$2,000\).
If a person is financing the car, though, an added variable complicates the calculation. The additional financing for the hybrid means that the person will pay more in interest. $10,000 more in financing at 5% per year is roughly $500 more in financing for that year. The principal is constantly being paid down by monthly payments, though, which reduces the amount of interest each month.
1.
A person is purchasing a car. They are considering a hybrid car or
a regular gas engine. They want to consider the cost of gas in their
purchase. They expect to drive the car for \(140,000\) miles before it breaks down or
they decide to sell it.
The hybrid car costs $38,000 and gets 40 miles per gallon.
The regular gas-only car costs $26,000 and gets 18 miles per gallon.
Assume gas costs \(\$4\) per gallon. Which car will be cheaper over \(140,000\) miles?
2. A person is purchasing a car. They are considering a hybrid car or a regular gas engine. They want to consider the cost of gas in their purchase. They expect to drive the car for \(140,000\) miles before it breaks down or they decide to sell it.
The hybrid car costs $39,000 and gets 38 miles per gallon.
The regular gas-only car costs $24,000 and gets 20 miles per gallon.
Assume gas costs \(\$4\) per gallon. Which car will be cheaper over \(140,000\) miles?
1. How would you describe the relationship between the gallons needed and the miles per gallon of a car in the above example? Is it a direct relationship, an inverse relationship, an exponential relationship, etc.?
2. What other financial factors might make a person more or less likely to buy a hybrid car?