A car rental agency is considering a modification in its oil change procedure. c

Question

A car rental agency is considering a modification in its oil change procedure. currently, it uses a type X filter, which cost $5and must be changed every 7,000 miles along with oil (5 quarts.) Between each oil change , one quart of oil must be added after each 1,000 miles. The proposed filter (typeY) has to be replaced every 5,000 miles (along with 5quarts of oil) but does not require any additional oil between filter changes. If the oil costs $1.08 per quart, what is the maximum acceptable price for the Type Y filter?

Explanation / Answer

In order to answer this question, you'll need a common baseline. One is given in 5,000 mile increments, the other in 7,000 mile increments. The lowest common multiple for these is 35,000, so set up the equations to figure out how much it will cost over 35,000 miles. Type X (35,000 miles) 5 filter changes + 25 quarts of oil (oil changes) + 30 quarts of oil between oil changes Type Y (35,000 miles) 7 filter changes + 35 quarts of oil (oil changes) Set these equal to one another with y being the price of the Type Y filter: 5(5) + 25(1.08) + 30(1.08) = 7y + 35(1.08) 84.4 = 7y + 37.8 7y = 46.6 y = 6.66 (rounded) The maximum acceptable price for Type Y filter is $6.66. Any higher than that, it's cheaper to go with Type X filter over the long run.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.