Math Problem how to Solve it

In our world today, many people around the globe go about their daily lives without ever knowing how much math is intertwined in their activities. From old granny Smith buying her groceries for the week, to little boy Tommy and his mom baking cookies for a school fundraiser, there is math in virtually everything we do. In the case of a family going on vacation, they will need to weigh in both of their options for an affordable and effective car rental plan.

An island car rental agency offers rental plans of interest to me for my one-week island vacation with my family. the first plan that I’ll call “PLAN A' provides me with a 2018 Jeep Renegade for a 150 dollar deposit for the week plus 40 cents per each mile driven. Another plan that I have been thinking of going with that I’ll call “PLAN B” provides me and my family with the same 2018 Jeep Renegade for a 110 dollar deposit for the week plus 65 cents per mile driven.

For the first plan, PLAN A, a deposit of 150 dollars is needed and an additional charge of 40 cents will be added on for every mile driven(150+0.40x). This means that for every mile I end up driving, 40 cents will be added to our expense on top of the 150 dollar deposit. The extra charge of 40 cents can represent a slope if we were to put things into a graph or equation.

BUT, we still have the other option that comes in the form of “PLAN B”

For PLAN B, a deposit of 110 dollars is needed with a charge of 0.65 cents for every additional mile driven (110+0.65x).

At this point, I would definitely be leaning towards PLAN A just because I would typically think that a bigger down payment would yield a smaller per mile fee!

If I were to go back and look at my two different options and the equations that I formed from them, they would produce a graph that shows two lines increasing upward representing how much I would end up paying for how many miles driven This table that I have been able to come up with shows the cost of driving a rental vehicle with a 40 mile increase at each calculation. PLAN A will be on the left half of the graph, and PLAN B on the right half.

Up until 160 miles are driven, PLAN B is clearly cheaper by a 30 dollar difference at best. However, the savings presented will start to fade away as I continue stacking up more mileage, and as soon as I drive 160 miles, the cost of both plans hit the same price of 214 dollars. Once 160 miles has been surpassed, PLAN A becomes the cheaper of the two plans, saving me 23 dollars at most over PLAN B.

Now in order for me to pick the best of these two plans, I need to keep in mind that I am on vacation with my family. I am going to assume that my family would want to travel around to the different tourist attractions that are offered here and truly get the most out of our trip so 160 miles may not be enough for my family over the period of time we are on vacation. I can see myself easily driving more than 200 miles while on vacation. using myself in real life as a fair example, I can drive over 300 miles a week by myself just going to college from my home and my parents can drive anywhere between 400 and 500 miles to get to work over a week. That’s already 800 miles a work week just coming and going so you can see that it isn’t unusual to pass a 160 mile mark.

Now that I have weighed in my options, I believe that PLAN A is the best car rental plan for me and my family. PLAN B would’ve been the clear winner if it was a day trip somewhere close to where I live, but since I would be on vacation here for five days, I will probably be doing a bit of driving around to the different attractions. The money I would save from PLAN A would give me the opportunity to buy things for my family such as souvenirs, food, show tickets and other fun things. The only reason renting PLAN B would be a better plan is if my family liked to walk down sidewalks and trails to destinations rather than driving and for the sake of my answer, I’m going to say that we would rather drive.

In conclusion, I think that everyone should go into the math when it comes down to these types of situations. It may not be the funniest thing in the world, but if it is just ignored, it could be that you end up on the short end of the stick.

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