Word problem Quantitative Reasoning Process

Question

 Manny is an online student who currently owns an older car that is fully paid for. He drives, on average, 110 miles per week to commute to work. With gas prices currently at $2.41 per gallon, he is considering buying a used fuel-efficient car, and wants to know if it would be good financial decision.

The old car Manny owns currently gets 17 miles per gallon for average fuel efficiency. It has been a great vehicle, but with its age, it needs repairs and maintenance that average $740 per year (as long as nothing serious goes wrong).

He is considering buying a newer used car that will cost a total of $7,000 over a three-year loan process. The used car gets 30 miles per gallon and would only require an average of $20 per month for general maintenance. To help make a decision Manny wants to calculate the total costs for each scenario over three years. He decides to use the quantitative reasoning process to do this.

Answer 1

Okay, this is several steps, but none of them are all that bad, really. Let's get organized and get started!

For both cars, we will be comparing total expenses over three years, so begin with the bucks and cancel / convert the other units.

Old: ($2.41/ 1 gal) * (1 gal/ 17 miles) * (110 miles / 1 week) * (52 weeks / 1 year) * 3 years = $2432.68

($740 / year)* 3 years = $2220

Total: $4652.68

Note that I put each unit in the opposite place it was in before to allow cancelling. 

New: $7,000

+ ($20/ 1 month) * (12 months / 1 year ) * 3 years = $720

+ ($2.41/ 1 gal) * (1 gal/ 30 miles) *(110 miles/week) *(52 weeks/year)*(3 years) = $1378.52

Total: $9098.52

The new car would nearly double his expenses for those three years, though after that -- when he fully owns the new car -- it will become half as costly.It will also save him lost work and other annoyances due to constant repairs (of the old car, I mean).