# 1. (3) My faucet runs at a rate of 5 gallons a minute. How many gallons a second is that?

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1 Math 137 Exam 2 Review Fibonacci Sequence and Chapters 6-10 NAMES: Show your work. Be sure to include appropriate units. 1. (3) My faucet runs at a rate of 5 gallons a minute. How many gallons a second is that? 2. (10) Maggie takes three of her friends on a car trip. They travel 535 miles. Their gas cost \$2.05 per gallon. Their car has a gas mileage of about 35 miles per gallon. They drove for a total of 8 hours. Find the following. a.) Number of gallons used b.) Total cost of gas c.) Passenger-miles d.) Total cost per passenger-mile e.) Average speed in miles per hour

2 3. (3) Consider the trip that Maggie and her friends took in the last question. In general, it is estimated to cost about 23 cents per mile to drive a car due to wear-and-tear (not including the gas). If she and her three friends want to share this cost for the trip, how much should each friend pay Maggie (not including that friend s portion for gas)? 4. (4) Kay wants to buy a new gas fireplace insert to replace her use of wood. She would normally burn two cords of wood in the winter. Wood costs \$260 per cord. She would like to know how much she can save by burning gas instead. Gas costs \$0.87 per 100,000 BTU. The fireplace insert would burn 30,000 BTU per hour. Kay figures she would need to turn on the fireplace for 6 hours per day for 120 days. The cost of installing the gas insert is \$120. How much will she save if she makes the switch? Show your work and include units along the way.

3 5. (12) Convert from metric to English or vice versa as indicated. The only metric-to-english conversions you are allowed to use are 1 meter equals feet and 1 gallon equals 3.79 liters. Of course, you may use any English-to-English conversions such as 1 mile equals 5,280 feet and any metric-to-metric conversions such as 1,000 meters equals 1 kilometer. a.) 35 m to feet b.) 170 feet to meters c.) 150 mi to kilometers d.) 4 ft to centimeters e.) 5 gallons to liters f.) 16 L to quarts

4 6. (4) Your speedometer is broken. You notice it takes you 48 seconds to travel between one mile marker and the next on the highway. What is your speed in miles per hour? If the speed limit is 65, are you speeding? 7. (3) Find the sum of the numbers below , (3) Use estimation to find a quick answer to the question. The city of Amberville has 33,542 citizens and it needs to build winter weather shelters. It wants to emulate a similar city to estimate the number of cots it needs. Their sister city has 52,678 citizens and has gotten by with 2,000 cots in its emergency shelters. How many cots should the city of Amberville provide? Show your work and explain your answer.

5 9. (4) Use physical manipulatives to solve this problem Here is a magic triangle. The sum of the digits forming each side of the triangle is 11. Use the digits 1, 2, 3, 4, 5, and 6 (once each) and find the proper locations for each. 10. (3) The Fibonacci sequence (from the pairs of rabbits problem) is reproduced below for the first several entries. Complete the next three entries and state, in words, the rule that assigns each entry. 1, 1, 2, 3, 5, 8, 13,,, 11. (3) The numbers below are in the Fibonacci sequence (separated by semicolons because there are commas in the numbers) but not starting at the beginning. Complete the next two entries. ; 46,368; 75,025; 121,393; ; ;

6 12. (3) Use guess-and-check to answer the following question. Include a well-labeled table with a clear explanation as to what you did. I accompanied a group of students to a play. Of the total number of students, 60% of them rode on a bus that had 75 seats. If the bus was full, how many total students went to the play? 13. (3) Use guess-and-check to answer the following question. Include a well-labeled table with a clear explanation as to what you did. A taxi will charge me \$2.35 plus \$0.45 per quarter-mile. If I have \$10 and want to give the driver a \$2 tip, how far (to the nearest quarter-mile) can I go? [You will have some leftover change.]

7 14. (4) List the sub-problems needed to answer the following problem. Then answer the problem. Picture a rectangular box with an end that is 5 inches high and 12 inches wide. That side has an area of 60 square inches (length times width). The top of this box is 324 square inches. The front of this box is 135 square inches. Assume all measurements are whole numbers. What is the volume of the box? [Remember that area is length times width and volume is length times width times height.] A picture of this box is provided.

8 15. (3) Use guess-and-check to answer the following question. Include a well-labeled table with a clear explanation as to what you did. Joe traveled 5 hours at an unknown rate. Marie took the same route (so traveled an equal distance) but traveled for 3 hours at 4 miles per hour faster than Joe. Find both Joe s and Marie s rates. [Hint: Distance equals rate times time.] 16. (3) My faucet drips one drop every two seconds. How many gallons of water does this leak waste in a year? [One quart of water is equal to about 18,927 drops. One gallon is equal to four quarts.]

9 17. (3) Estimate the area of the figure below. The grid lines are spaced every 1 inch. Explain your answer.

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1 Which factors represent 7? 7 7 7 7 7 7 7 7 7 7 1 1 The sizes of drill bits are inch, 1 inch, 1 inch, and 1 16 inch. Which shows these sizes in correct order from smallest to largest?, 1, 1, 1 16 1,,