math

Bunker Hill Community College | MAT 097 Foundations of Algebra

Name: _________________________ Section: MAT097-

MAT097 FINAL EXAM (FORM B)

A scientific calculator is permitted. Cellphones may not be used as calculators. Each question will be graded in accordance with the rubric attached at the end of this test. Show all work on the test or on the work paper provided. The minimum passing grade is 70%. You have one chance to retake the exam.

1. Simplify the expression (5 points): [4(𝑥 − 4) − 9] + [6(𝑥 − 1) + 6]

2. Solve the equation (5 points): x - x = x + 134 1 2

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3. The equation 𝑦 = 0.001𝑥 + 0.10 can be used to determine the approximate profit, y in dollars, of producing x items. (5 points)

a) Solve for x in terms of y.

b) How many items must be produced so the profit will be at least $398?

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Bunker Hill Community College | MAT 097 Foundations of Algebra

4. A busload of campers stopped at a local organic dairy stand for ice cream. They ordered 91 cones, some soft-serve at $2.25 each and the rest hard-pack at $0.75 each. The total bill was $158.25. How many of each type of cone were ordered? (10 points)

5. Two vans of BHCC students leave the campus at the same time, both headed along the same route to New York for a service project. A professor is driving one of the vans at an average of 40 mph. A BHCC student is driving another van at an average of 61 mph. How long will it take for the two vans to be 63 miles apart? (5 points)

6. Ali must average 90 on all 5 quizzes in order to earn an A in her MAT097 Foundations of Algebra class. She scored 90, 87, 93 and 85 on the first 4 quizzes. What is the least she must score on the fifth quiz in order to get an A? (5 points)

7. Mrs. Boyd has a desk full of quarters and dimes. If she has a total of 54 coins with a total face value $12.30, how many of the coins are quarters? (5 points)

8. The temperature at the South Pole was 1˚F at 8:00AM. At 2:00PM, it was -35˚F. By how many degrees did the temperature drop? Predict the temperature at 5:00PM, if the decline remains constant. (5 points)

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Bunker Hill Community College | MAT 097 Foundations of Algebra

9. Rosie’s Bakery just purchased an oven for $1,970. The owner expects the oven to last for 10 years with a constant depreciation each year. It can then be sold as scrap for an estimated salvage value of $270 after 10 years. (20 points) a) Find a linear equation modeling the value of the oven, y, after x years of use.

b) Find the value of the oven after 2.5 years.

c) Find the y-intercept. Explain the meaning of the y-intercept in the context of this problem.

d) Graph the equation of the line. Be sure to label the axes.

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Bunker Hill Community College | MAT 097 Foundations of Algebra

10. It takes Michelle 25 minutes to descend 850 feet of the beginner slope at Mount Washington. (5 points) a) Find her rate of descent (slope).

b) If Michelle begins her descent at a height of 1200 feet, find a linear equation to describe her skiing motion.

11. A laboratory technician at Beth Israel Hospital needs to make a 10-liter batch of antiseptic that is 60% alcohol. How can she combine a batch of antiseptic that is 30% alcohol with another variety that is 70% alcohol to formulate the desired concentration? (10 points)

12. A FEMA plane is carrying bottled water and cases of medicine to victims of Hurricane Sandy. Each bottle of water weighs 10 pounds and each case of medicine weighs 15 pounds. The plane can carry a maximum of 50,000 pounds of cargo. a) Write an inequality that expresses the plane’s weight limitation in terms of the number of bottles of water, w, and the number of cases of medicine, m, in the plane (5 points)

b) Graph this inequality. (5 points)

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Bunker Hill Community College | MAT 097 Foundations of Algebra

13. Earth is approximately 93,000,000 miles from the Sun, and Jupiter is approximately 484,000,000 miles from the Sun. Assume that Sun, Earth and Jupiter are on the same straight line:

How long would it take the Vikranta spaceship traveling at 7,500 mph to fly from Earth to Jupiter? Express the answer in scientific notation to two decimal places. (5 points) (Hint: Find the distance from Earth to Jupiter, then use 𝑡 = 𝑑/ 𝑟 where t is time, d is distance and r is rate)

14. Supply is the amount of a specific product available for purchase. Demand is the consumer's desire and willingness to pay a certain price for the product. Suppose that Qs represents the quantity of Tshirts supplied and Qd represents the quantity of T-shirts demanded at a concert. The equations below show how each quantity is related to the price (P)of a T-shirt:

Quantity Supplied: Qs = 5P – 150 Quantity Demanded: Qd = -5P + 50

The equilibrium price is defined as the price at which quantity supplied EQUALS quantity demanded. Find the equilibrium price for T-shirts at this concert. Solve using any algebraic method or, if you solve by graphing, be sure to label the axes. (5 points)

BONUS QUESTION (5 points): Solve: (𝑥 + 2) + 6 > 2𝑥 + 5(𝑥 + 1)

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