Answer:
Step-by-step explanation:
I'm assuming just number 7 because I can't see anything before that. I will not just answer, but I'd be happy to work you through all you need.
First might want to note what the fuel level is exactly that they refuel. Since the total is 14, we want it to be at a fourth for when they refill. so 17/4 or 4.25.
Since we are given a range of miles per gallon and price, it might be best to average everything out to estimate the results. you could do that before or after getting the equation. If you averaged before, the aerage miles per gallon would be (25+29)/2 and the average price would be (3.47+3.69)/2
Anyway, there are two parts. How many times they stop and how much they spend. First, we want to realize they will always buy the same amount of gas. THey want to fill the tank, and since it has 17 total but they wait until it is at 4.25, how much will they fill each time? It's a difference problem so 17-4.25. Let's call this F. The price then is F times the price per gallon. Either use the average value from before or take it for the lowest and the highest price then average that. So now, when we find the number of stops, we just multiply by this Number, Let's call it P. Also let's call number of stops S
So now we have F = 17-4.25 and P = S*F*(3.47+3.69)/2
Now, we want to find S. On a full tank of 17 gallons, how far can they go? Well, at 25 mpg, each gallon gives 25 miles so that's 25*17. Though that's only if we use the full tank. We are only going to use F gallons of gas. so at 25 mpg, we are going to get 25F miles. Similarly 29 mpg will get us 29F miles. Let's average those to get an estimation. We will Call this D, so D = (25F+29F)/2. Probably noticed this isn't S. Well S is a little complicated to figure out.
Let's say you could go 10 miles before refilling. how many stops would 9 miles be? None. How many would 9.9 be? None still. You could go all the way to 9.9999999... technecally and still not stop. So we have to take this into account. We can go D Miles on average. So if m is less than D, there is no stop needed. If you are unfamiliar with the floor function let me know, but that's the first option that comes to mid. Bascially what the floor function does is round down to the nearest integer. so 3.1 would be 3, 3.5 would be 3 and even 3.9 would be 3. So what that would look like is a bracket with the upper nubby erased. (ceiling function is the opposite with the bottom nubbies erased.) so [ but with the top part gone so it looks like an L. I will just write it like this floor(x).
Now, the floor function we want to find is m/D. This will tell us the stops needed. if m is less than D then the floor function goes down to 0. if it is just slightly over D the floor function will go don to 1, and so on. Do let me know if that doesn't make sesne. Anyway, S = floor(m/D) And with that you can answer the question. of course, S is the number of times they stop. I will also say if your class does not want you to use the floor function you can go without it, you just won't get the exact amount except if you go some multiple of D miles. so m would need to equal D, 2D, 3D or something.
b) b is easy because of all the work before. just plug in m. Keep in mind though it's a round trip so you are going m miles twice.
