Question

A car rental agency is considering a modification in its oil change procedure.​ Currently, it uses a Type X​ filter, which costs ​$5 and must be changed every 9 comma 000 miles along with the oil ​(5 ​quarts). Between each oil​ change, one quart of oil must be added after each 500 miles. The proposed filter​ (Type Y) has to be replaced every 7 comma 000 miles​ (along with 5 quarts of​ oil) but does not require any additional oil between filter changes. If the oil costs ​$1.09 per​ quart, what is the maximum acceptable price for the Type Y​ filter?

Answer 1

The maximum acceptable price would be $16.24

Step-by-step explanation:

In order to solve this problem we have to create an equation, and equalize both prices, so the price of the filter will be expressed by "y".

We know that the X filter costs $5 and must be changed every 9,000 miles, with the oil 5 quartz, and one quart of oil must be added every 500 miles, the resultant equation for the price of those 9,000 miles is:

`(5+ 5(1.09)+16(1.09))/(9000)`

And to express the new oil it would be:

`(x+ 5(1.09)+)/(7000)`

So we just have to equalize them:

`(x+ 5(1.09)+)/(7000)=(5+ 5(1.09)+16(1.09))/(9000)\\9000x+49,050=195,230\\9000x=195,230-49,050=146,180\\x=(146180)/(9000) \\x= 16.2422`

So we know that the maximum price that the new oil filter would be $16.2422 because at that point it costs the same as the other filter witht he cost of the adding of the oil quarts.