Math 154A Elementary Algebra

Transcription

1 Math 154A Elementary Algebra Study Guide for Exam 3 Exam 3 is scheduled for Thursday, October 30 th. You may use a 3" x 5" note card (both sides) and a scientific calculator. You are expected to know (or have written on your note card) any formulas you may need. You will be asked to define variables and set up equations. Full credit will not be given for just a correct answer. No charts or formulas will be provided on the exam. Think about any formulas you needed for homework. For example: d=rt, i=prt, quantitiy x price per item = value; sum of angles in a triangle is 180 degrees, sum of two complementary angles is 90 degrees, etc... For Exam 3 you will need to be able to: 1. Translate phrases into mathematical expressions, express the relationship between two related quantities, translating applications into equations. 3.1 a subtracted from b means b-a 2. Solve an application problem by defining a variable, writing an equation that represents the relationship in the problem, solving the equation and answering the question asked. The problems in this section had no underlying formula. 3.2 amount of money in quarters amount of money in nickels interest gainedfrom $x dollarsinvestedat 11% amount of money total interest gainedfrom $(x4000)investedat 12% constant payment payment per hour constant payment payment per hour totalinterest gainedfrom both acountsfor 1year 3. Solve a geometric problem by defining a variable, determining which geometric fact to use, writing an equation, solving the equation, and answering the question. No charts or formulas will be provided on the exam so be sure to write them on your index card. 3.3 perimeter 2 times thelength 2 times thewidth right angle another angle measure of anglea measure of angleb oneangle sumof all angles 4. Solve an application problem by defining a variable, writing an equation that represents the relationship in the problem, solving the equation and answering the question asked. These problems may involve interest, mixture, and motion. 3.4 faster's distance slower'sdistance totaldistanceapart faster's distance slower' s distance totaldistancetraveled 3 poundsfor $3.60each 2 poundsfor $4.80each 5 poundsfor $x each x liters of 8%solution 6 liters of15%solution x6 liters of12%solution

2 Math 154A Chapter 3 Exam Review Name 1. Express the quotient of a number and Express the difference of a number and Express five percent of a number. 4. Write the expression: five subtracted from a number. 5. Express the monetary value of x number of quarters. 6. Write the decimal as a percent. 7. Write the expression: three less than a number. 8. Write the expression: one-third the distance, d. 9. Define the variable and express the related quantity in terms of that variable for the following statement: The length is 3 more feet than twice its width. 10. A 40-foot board is cut into two pieces. If L is the length of one piece, use L to represent the other piece. 11. The sum of two numbers is 13. One number is k. Express the other number in terms of k. 12. If you had x liters of red liquid, added a certain amount of blue liquid, and obtained 20 liters of purple liquid, express the number of liters of blue liquid that was added in terms of x. 13. Together, the cost of a meal and a 9% tax is $ Find the cost of the meal before the tax was included.

3 14. Say your GPA increased by 2%, and is now 3.4. What was your GPA before? (round to the nearest tenth) 15. Five subtracted from 3 times a number is 22. Find the number. 16. Mary is 20 years older than her son Bob. In 7 years the sum of their ages will be 44. How old are they now? 17. If you got paid a flat rate of $80 for the first 8 hours on a job and $15/hr for each additional hour, how many hours did you work total if you got paid $125 that day? 18. The sum of two consecutive integers is 175. Find the numbers.

4 19. Say you have $2.95 in nickels and dimes. If you have 4 more dimes than nickels, how many nickels and dimes do you have? 20. Say you deposited money into one account that pays 5% interest and $1200 less than that amount into an account that pays 4% interest. After 1 year the total interest earned for both accounts was $141. Find the amount that was deposited into each account. 21. Joe Traveler only used two-thirds as many gallons of gas driving back from his vacation as he did going to it. Driving both directions, he used a total of 60 gallons of gas. How many gallons did he use driving each way on his vacation destination?

5 22. A bartender and a waitress needed to split the tip jar, which had $269 in it. The bartender always gets $15 less than the waitress. How much do they each get? 23. The perimeter of a rectangle is 36 yards. The width is 18 yards less than twice the length. Find the length and width of the rectangle 24. You want to build a fence around a rectangular region. You have enough fencing for 800 feet around, and you know that you want the length to be 2/3 the width. What are the length and width?

6 25. Say you are going to build a fence next to a river. You want the length to be 60 feet more than 3 times the width, but you only have 740 feet of fencing available. Find the length and width. Width Length 26. Company A charges $750 plus $20 for each widget. Company B charges $900 plus $12.50 for each widget. a. How many widgets would it take for both companies to cost the same? b. If you were going to purchase 21 widgets, which company would be cheaper? 27. How many ounces of 20% and 90% alcohol should you mix together to obtain 14 ounces of 40% alcohol?

7 28. If French roast coffee sells for $7.50 per pound and vanilla hazelnut coffee sells for $11.50 per pound, how many pounds of vanilla hazelnut should you mix with 12 pounds of French roast to get a blend that is sold for $10 per pound? 29. Say you were famous and the paparazzi were chasing you. You re running 12 miles an hour, and they re running 10 miles an hour. You get to your house, and they are 1 mile behind. How long did it take to get home? You Paparazzi Rate Time Distance 30. Two cars are 225 miles apart. They start traveling towards each other at the same time, but one car is going 5 miles an hour faster than the other. If it took 3 hours for the cars to pass each other, what was each car s rate? Rate Time Distance

8 Answers: x x x 4. x x % 7. x d 3 9. Let w width Then 2w 3 length 10. Let L one piece Then 40 L other piece 11. Let k one number Then 13 k other number 12. Let x liters of red liquid Then 20 x liters of blue liquid 13. The meal was $25 before tax 14. Your GPA was about 3.3 before increase 15. The number is Bob is 5 years old and Mary is 25 years old 17. You worked 3 extra hours for a total of 11 hours 18. First number is 87 and the next consecutive number is You have 17 nickels and 21 dimes 20. There is $2100 in the 5% account and $900 in the 4% account 21. He used 36 gallons going there and used 24 gallons coming back 22. The waitress gets $142 and the bartender gets $ The length is 12 yards and the width is 6 yards 24. The width is 240 feet and the length is 160 feet 25. The width is 136 feet and the length is 468 feet 26. a.) It takes 20 widgets for both companies to cost the same. b.) Company B charges $1,162.50, which is cheaper than Company A, which is $1, It took 10 ounces of 20% alcohol and 4 ounces of 90% alcohol 28. You should mix 20 pounds of vanilla hazelnut to get a 32 pound blend 29. It took ½ hour to get home 30. The slower car travels at 35 mph and the faster car travels at 40 mph