ALGEBRA edited Flashcards
Spartan Stadium at San Jose State University in California has a seating capacity of about 30,000. A newspaper article states that the Spartans get four times as many tickets as the visiting team. Suppose S represents the number of tickets for the Spartans and V represents the number of tickets for the visiting team’s fans. Which system could be used by a newspaper reader to determine how many tickets each team gets?
ANS: (S-4V=0), (S+V=30000)
The first Earth Day was observed on April 22, 1970. Since then, the week of April 22 has been Earth Week, a time for showing support for environmental causes. Fans Café is offering a reduced refill rate for soft drinks during Earth
Week for anyone purchasing a Fans mug. The mug costs $2.95 filled with 16 ounces of soft drink. The refill price is 50¢. A 16-ounce drink in a disposable cup costs $0.85. What is the approximate break-even point for buying the mug and refills in comparison to buying soft drinks in disposable cups?
(7, 5.95)
As an incentive plan, a company stated that employees who worked for four years with the company would receive $516 and a laptop computer. Mr. Rodriquez worked for the company for 3.5 years. The company pro-rated the incentive plan, and he still received the laptop computer, but only $264. What was the value of the laptop computer?
$1,500
Ana Colón asks her broker to divide her 401K investment of $2000 among the International Fund, the Fixed Assets Fund, and companionship y stock. She decides that her investment in the International Fund should be twice her investment in company stock.
During the first quarter, the International Fund earns 4.5%, the Fixed Assets Fund earns 2.6%, and the company stock falls 0.2%. At the end of the first quarter, Ms. Colón receives a statement indicating a return of $58 on her investment.
How did the broker divide Ms. Colón’s initial investment?
International Fund $1200;
Fixed Assets Fund $200;
company stock $600
Aluminum alloy is used in airplane construction because it is strong and lightweight. A metallurgist wants to make 20 kilograms of aluminum alloy with 70% aluminum by using two metals with 55% and 80% aluminum content.
How much of each metal should she use?
8 kg of the metal with 55% aluminum and
12 kg of the metal with 80% aluminum
In 1990, the Americans with Disabilities Act (ADA) went into effect. This act made provisions for public places to be accessible to all individuals, regardless of their physical challenges. One of the provisions of the ADA is that ramps should not be steeper than a rise of 1 foot for every 12 feet of horizontal distance.
A. What is the slope of such a ramp?
B. What would be the maximum height of a ramp 18 feet long?
A) ANS: 1/12 or approximately 0.0833
B) ANS: 1.5 ft
The Band Boosters want to open a craft bazaar to raise money for new uniforms. Two sites are available. A Main Street site costs $10 per square foot per month. The other site on High Street costs $20 per square foot per month.
Both sites require a minimum rental of 20 square feet. The Main Street site has a potential of 30 customers per square foot, while the High Street site could see 40 customers per square foot. The budget for rental space is $1200 per month. The Band Boosters are studying their options for renting space at both sites.
A. Determine what function would represent the possible number of customers per square foot at both locations.
A) ANS: f(x,y) = 30x + 40y
The Band Boosters want to open a craft bazaar to raise money for new uniforms. Two sites are available. A Main Street site costs $10 per square foot per month. The other site on High Street costs $20 per square foot per month.
Both sites require a minimum rental of 20 square feet. The Main Street site has a potential of 30 customers per square foot, while the High Street site could see 40 customers per square foot. The budget for rental space is $1200 per month. The Band Boosters are studying their options for renting space at both sites.
B. If space is rented at both sites, how many square feet of space should the Band Boosters rent at each site to maximize the number of potential customers?
B) ANS: 80 ft^2 at the Main St. site and 20 ft^2 at the High St. site
Woodland Bicycles makes two models of off-road bicycles: the Explorer, which sells for $250, and the Grande Expedition, which sells for $350. Both models use the same frame, but the painting and assembly time required for the Explorer is 2 hours, while the time is 3 hours for the Grande Expedition. There are 375 frames and 450 hours of labor available for production.
How many of each model should be produced to maximize revenue?
225 Explorers,
0 Grande Expeditions
Angela’s Pizza is open from noon to midnight each day. Employees work 8-hour shifts from noon to 8 P.M. or 4 P.M. to midnight. The store manager estimates that she needs at least 5 employees from noon to 4 P.M., at least 14 employees from 4 P.M. to 8 P.M., and 6 employees from 8 P.M. to midnight. Employees are paid $5.50 per hour for hours worked between noon and 4 P.M. The hourly pay between 4 P.M. and midnight is $7.50.
A) Write a function to represent the daily cost of payroll.
B) Find the number of day-shift workers and night-shift workers that should be scheduled to minimize the cost.
C) What is the minimal cost?
A) ANS: C(n,d) = 52d + 60n
B) ANS: 8 day-shift and 6 night-shift workers
C) ANS: $776
Ms. Carlyle has written a final exam for her class that contains two different sections. Questions in section I are worth 10 points each, and questions in section II are worth 15 points each. Her students will have 90 minutes to complete the exam. From past experience, she knows that on average questions from section I take 6 minutes to complete and questions from section II take 15 minutes. Ms. Carlyle requires her students to answer at least 2 questions from section II. Assuming they answer correctly,
how many questions from each section will her students need to answer to get the highest possible score?
10 section-I questions, 2 section-II questions
Diego wants to invest up to $11,000 in certificates of deposit at First Bank and City Bank. He does not want to deposit more than $7,500 at First Bank. He will deposit at least $1,000 but not more than $7,000 at City Bank. First Bank offers 6% simple interest on deposits, while City Bank offers 6 1/2% simple interest.
How much should Diego deposit into each account so he can earn the most interest possible in one year?
$4000 in First Bank, $7000 in City Bank
A potato chip company makes chips to fill snack-size bags and family-size bags. In one week, production cannot exceed 2,400 units, of which at least 600 units must be for snack-size bags and at least 900 units must be for family size. The profit on a unit of snack-size bags is $12, and the profit on a unit of family-size bags is $18.
How much of each type of bag must be processed to maximize profits?
600 units of snack size,
1800 units of family-size
Mr. Perez has an auto repair shop. He offers two bargain maintenance services, an oil change and a tune-up. His profit is $12 on an oil change and $20 on a tune-up. It takes Mr. Perez 30 minutes to do an oil change and 1 hour to do a tune-up. He wants to do at least 25 oil changes per week and no more than 10 tune-ups per week. He can spend up to 30 hours each week on these two services.
What is the most Mr. Perez can earn performing these services?
$720
Martina knows that her monthly telephone charge for local calls is $13.65 (excluding tax) for service allowing 30 local calls plus $0.15 for each call after. Write an equation to calculate Martina’s monthly telephone charges and find the cost if she made 42 calls.
C = $13.65 + $0.15(n - 30); $15.45
A manufacturer makes a profit of $6 on a bicycle and $4 on a tricycle. Department A requires 3 hours to manufacture the parts for a bicycle and 4 hours to manufacture parts for a tricycle. Department B takes 5 hours to assemble a bicycle and 2 hours to assemble a tricycle.
How many bicycles and tricycles should be produced to maximize the profit if the total time available in department A is 450 hours and in department B is 400 hours?
50 bicycles, 75 tricycles
Amanda’s teacher calculates grades using a weighted average. She counts homework as 10%, quizzes as 15%, projects as 20%, tests as 40%, and the final exam as 15% of the final grade. Going into the final, Amanda has scores of 90 for homework, 75 for quizzes, 76 for projects, and 80 for tests.
What grade does Amanda need on the final exam if she wants to get an overall grade of at least an 80?
x > 83.5
A cable company wants to provide service for residents of an island. The distance from the closest point on the island’s beach, point A, directly to the mainland at point B is 2 kilometers. The nearest cable station, point C, is 10 kilometers downshore from point B. It costs $3500 per kilometer to lay the cable lines underground and $5000 per kilometer to lay the cable lines under water. The line comes to the mainland at point M.
At what distance x should the cable come to shore to minimize cost?
1.96 km from point B
The Eastern Minnesota Paper Company can convert wood pulp to either newsprint or notebook paper. The mill can produce up to 200 units of paper a day, and regular customers require 10 units of notebook paper and 80 units of newsprint per day.
If the profit on a unit of notebook paper is $400 and the profit on a unit of newsprint is $350, how much of each should the plant produce?
120 units of notebook and 80 units of newsprint
Jon played in two varsity basketball games. He scored 32 points by hitting 17 of his 1-point, 2-point, and 3-point attempts. He made 50% of his 18 2-point field goal attempts. Find the number of 1-point free throws, 2-point field goals, and 3-point field goals Jon scored in these two games.
5 free throws, 9 2-point field goals, 3 3-point field goals
Electricity Wires used to connect electric devices have very small resistances, allowing them to conduct currently more readily. The resistance R of a piece of wire varies directly as its length L and inversely as its cross sectional area A. A piece of copper wire 2 meters long and 2 millimeters in diameter has a resistance of 1.07x10^-2 ohms.
Find the resistance of a second piece of copper wire 3 meters long and 6 millimeters in diameter.
1.78 x 10^-3 ohms
The speed of the current in Puget Sound is 5 miles per hour. A barge travels with the current 26 miles and returns in 10 2/3 hours. What is its speed in still water?
8 mph
Yhe semester test in your English class consists of short answer and essay questions. Each short answer question is worth 5 points, and each essay question is worth 15 points. You may choose up to 20 questions of any type to answer. It takes 2 minutes to answer each short answer question and 12 minutes to answer each essay question.
A. You have one hour to complete the test. Assuming that you answer all of the questions that you attempt correctly, how many of each type should you answer to earn the highest score?
B. You have two hours to complete the test. Assuming that you answer all of the questions that you attempt correctly, how many of each type should you answer to earn the highest score?
A) ANS: 18 short answer and 2 essay for a score of 120 points
B) ANS: 12 short answer and 8 essay for a score of 180 points
