Unit 1 ProjectProblem Solving

You have worked with unit costs to find the best deal and to compare different costs of similar items. The question for this project is: How much do you spend on fuel per month to get to and from work/school or other place that you drive to regularly?

You are going to look at different ways of using unit costs in order to answer this question.

Warm up: One thing many people don't realize is that rates can be expressed in more than one way. For example, 12 inches per 1 foot ( is equivalent to 1 foot per 12 inches ( This is important because sometimes when we do unit costs or unit analysis, the units are not in the right spots in the initial rate and we must recognize that we can "flip it" if needed. So to practice that. Write each rate in 2 equivalent fractional forms, the first one has been done for you:

1. 15 steps per 4 yards:
2. $8 per 15 cookies
3. 35 miles per 1 gallon
4. $286 per credit hour

1. For the first part of this project, we are all going to use the same vehicle to do our computationsan awesome Grand Caravan Minivan. This particular vehicle is gray, has 102,000 miles on it, has a 3.6 L engine and a combined city/highway gas mileage rating is 22 miles per gallon. It has a 20-gallon tank capacity, 283 horsepower and can tow 3,600 pounds. There are many other great features.

Use Polya's 4-step process for problem solving to find the cost per mile for driving this vehicle.

1. Step 1: Understand the Problem
   1. What information given in the problem is necessary to answer the question?
   2. What information given in the problem is unnecessary to answer the question?
   3. What information is missing that is needed to answer the question? State the value(s) that you will use for the missing information.
   4. Step 2: Devise a Planthree students discussing their plans state:

Bo: "The tank holds 20 gallons of gas and if I fill that up once a week, I need to take the cost of a gallon of gas times 20 gallons to figure out how much a tank of gas costs. Then I can divide that by the miles driven that week to find the cost per mile."

Agaba: "Since the gas mileage is 22 miles per gallon that also means that it can be expressed as 1 gallon per 22 miles. I would then take the cost of a gallon of gas and times that by 1 gallon per 22 miles, and that would give me the cost per mile."

Tyne: "I would just need to take the cost of one gallon of gas and divide that by the gas mileage of 22 miles per gallon since each of the initial rates are per gallon. That would give the value for the cost per mile."

Which, if any, of the students have a plan that will give the cost per mile?

Bo_____ Agaba_____ Tyne_____ None of these students are correct____

Explain your reasoning:

1. Step 3: Carryout the Plancompute the cost per mile for driving this vehicle. Show your work including units and label your answer (round your final answer to 5 decimals if necessary).
2. Step 4: Lookback and check the answerdid you answer what was being asked, is your answer reasonable? Check your answer by taking your cost per mile from the above question and multiplying it by 22 miles per gallon. Show your work below. This should give you the cost per gallon of gas that you selected. If it doesn't, go back to step c and check your computations and set upyou might need to try an alternative method.
3. Using your answer for the cost per mile from above, compute what it would cost you per month in fuel to get to and from your destination (work/school/other). Fill in the chart below to help keep your information organized. Show your work along with the unit analysis and labels.

	Minivanusing cost per mile
Type of vehicle	Grand Caravan
Combined miles per gallon	22 miles per gallon
Cost per mile (computed above)
Your destination (work/school/other)
Round-trip distance for your destination
Number of times you go to this destination per month.

1. Another way to approach the question of How much do you spend on fuel per month to get to and from work/school or other place that you drive to regularly,is to figure out how much it costs per round trip for your destination. Use Polya's four-step process and the prompts below to compute the cost per round trip.
   1. Using your round-trip distance and the given gas mileage of the minivan, compute how many gallons of fuel it takes for you to make one round trip to and from your destination (gallons per trip). Show work with unit analysis and label your final answer.
   2. Using your number of gallons of fuel per trip from above and the cost of a gallon of gas to compute the cost per trip. Show work with unit analysis and label your answer.
   3. Now, use your cost per trip and the number of times you make that trip per month from the table above to compute the cost per month to drive to and from work/school/other. Show work with unit analysis and label your answer.
2. Compare your answer from #3c to your answer from #2.
3. When problem solving, there can be many ways to solve a problem. What is important to keep in mind when you are problem solving, no matter the method you choose?
4. Finally, use your current vehicle (if you do not have a vehicle, you can research any vehicle you like) to compute the cost of driving to and from work/school/other. You are free to solve this any way you choose.
5. Predict what you think the cost per month will be
6. List all necessary information below
7. Show ORGANIZED work with unit analysis and labelsyou can organize it however you like (table, hand write it and insert an image, type it, write it out in paragraph form, etc.)
8. Compare your computed value to your predicted value