Semester 1 Warm-Ups

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Transcript of Semester 1 Warm-Ups

  • 1. Algebra 2WARM-UP 1 WORD PROBLEM WARM-UP 1How long will it take 100 storks to catch 100 frogs,when five storks need five minutes to catch five frogs?Answer: 5 minutes.

2. Algebra 2WARM-UP 2 WORD PROBLEM WARM-UP 1Logan, Vikrant and Emily differ greatly in height.Vikrant is 14 taller than Emily. The difference betweenVikrant and Logan is two inches less than between Loganand Emily. Vikrant at 6-6 is the tallest of the three.How tall are Logan and Emily?Answer: If Vikrant is 6-6, then Emily must be 5-4,and Logan must be 6-0 (8 greater than Emily and 6less than Vikrant). 3. Algebra 2WARM-UP 3 WORD PROBLEM WARM-UP 1Find the numbers that will replace letters a and b sothat the five-digit number will be divisible by 36: 19a 9b(Note: There are two possible solutions)Answer: 19692 and 19296. To be divisible by 36, anumber must be divisible by 9 and 4. To be divisible by9, the sum of the digits must be divisible by 9. The lasttwo digits must be divisible by 4. Therefore, b can beeither 2 or 6. 4. Algebra 2WARM-UP 4 WORD PROBLEM WARM-UP 1On the way home from school, Tom found out that hegot only half the allowance that Mark got. Suzi is threeyears older and receives three times what Tom gets.Together, the three receive $144. How much is eachstudent getting?Answer: Divide the total by 6: 144/6 =24. ThereforeTom gets $24; Mark gets $48; and Suzi receives $72. 5. Algebra 2WARM-UP 5 WORD PROBLEM WARM-UP 1Students in class with less than 30 students finishedtheir algebra test. 1/3 of the class received a B, received a B-, and 1/6 received a C. 1/8 of the classfailed. How many students received an A.Answer: There were 3 As. Look for a commondenominator the only one smaller than 30 is 24. Whenyou add up the known fractions, you have 21/24. 6. Algebra 2 WARM-UP 6 WORD PROBLEM WARM-UP 1On a road 75 miles long, two trucks approach eachother. Truck A is traveling at 55 mph while Truck B istraveling at 80 mph. What is the distance between thetwo trucks one minute before they collide?Answer: 2.25 miles. The trucks are approaching eachother at a speed of 135 mph (55 + 80). 135/60=2.25 7. Algebra 2 WARM-UP 7WORD PROBLEM WARM-UP 1Ten years more than three times Charlies age is twoyears less than five times his age. How old is he?Answer: 6 years. 8. Algebra 2WARM-UP 8WORD PROBLEM WARM-UP 1The average age of the three Wilson children is 7 years.If the two younger children are 4 years old and 7years old, how many years old is the oldest child?Answer: 10 years. 9. Algebra 2 WARM-UP 9WORD PROBLEM WARM-UP 1A box of 100 personalized pencils costs $30. How manydollars does it cost to buy 2500 pencils?Answer: $750. 10. Algebra 2WARM-UP 10WORD PROBLEM WARM-UP 1Jeff has an equal number of nickels, dimes and quartersworth a total of $1.20. Anne has one more of eachtype of coin than Jeff has. How many coins doesAnne have? If x y = 6 and x + y = 12, what is the value ofy?Answer: 12 coins. 11. Algebra 2 WARM-UP 11WORD PROBLEM WARM-UP 1Alex has fifteen nickels and dimes. He has seven morenickels than dimes. How many of each coin does he have?Answer: 11 nickels and 4 dimes.If x y = 6 and x + y = 12, what is the value of y?n d 15n d 7(d 7) d 152d 7 15d 4 12. Algebra 2WARM-UP 12WORD PROBLEM WARM-UP 1Joel has two fewer quarters than dimes and a total offourteen dimes and quarters. How many of each coindoes he have?Answer: 8 dimes and 6 quarters.q d 2 If x y = 6 and x + y = 12, what is the value ofy? q d 14 (d 2) d 14 2d 2 14 d 8 13. Algebra 2 WARM-UP 13WORD PROBLEM WARM-UP 1Ten years more than three times Charlies age is twoyears less than five times his age. How old is Charlie?Answer: 6 years old. 3C 10 5C 2If x y = 6 and x + y = 12, what is the value of y? 14. Algebra 2WARM-UP 14WORD PROBLEM WARM-UP 1When Alice is three times as old as she was five years ago, she will be twice her present age. How old is she?Answer: 15 years old. 3(A 5) 2A If x y = 6 and x + y = 12, what is the value ofy? 15. Algebra 2 WARM-UP 15 WORD PROBLEM WARM-UP 1The sum of Garys and Vivians ages is twenty-threeyears. Gary is seven years older than Vivian. How old iseach person?Answer: Vivian 8 years; Gary - 15 years. G V 23G V 7 V (V 7) 23 V2 7 23 16. Algebra 2 WARM-UP 16 WORD PROBLEM WARM-UP 1Brad is five years younger than Louise. The sum of theirages is thirty-one years. How old is each person?Answer: Brad 13 years; Louise 18 years. B L 5 B L 31(L 5) L 312L 5 31 17. Algebra 2WARM-UP 17 WORD PROBLEM WARM-UP 1The sum of the ages of Juan and Herman is twenty-fouryears. Juan is twice as old as Herman. How old is each?Answer: Juan 16 years; Herman 8 years. J H 24J 2H(2H ) H 243H 24 18. Algebra 2 WARM-UP 18WORD PROBLEM WARM-UP 1If Edith were five years older, she would be twiceFreds age. If she were three years younger, she wouldbe exactly his age. How old is each one?Answer: Edith 11 years; Fred 8 years.E 5 2FE 3 FE 5 2(E 3)E 5 2E 6 19. Algebra 2 WARM-UP 19WORD PROBLEM WARM-UP 1When Leonard is five years older than double hispresent age, he will be three times as old as he was ayear ago. How old is he?Answer: Leonard 8 years. 2L 5 3(L 1) 2L 5 3L 38L 20. Algebra 2 WARM-UP 20 WORD PROBLEM WARM-UP 1If Karen were two years older than she is, she would betwice as old as Larry, who is eight years younger thanshe. How old is each?Answer: Karen 18 years; Larry 10 years.2L 5 3(L 1)2L 5 3L 3 21. Algebra 2WARM-UP 21WORD PROBLEM WARM-UP 1Yolanda has a total of thirty-seven nickels and dimes.The dimes come to 40 more than the nickels. How manyof each coin does she have?Answer: 22 nickels; 15 dimes. n d 3710d 5n 40 nn 4 37 2 22. Algebra 2 WARM-UP 22 WORD PROBLEM WARM-UP 1Sue has a total of forty nickels and dimes. She has twomore dimes than nickels. If she had eleven more coins,she would have 90 more. How many nickels and dimesdoes she have?Answer: 19 nickels; 21 dimes.n d 40d n 2 n (n 2) 40 23. Algebra 2 WARM-UP 23 WORD PROBLEM WARM-UP 1Lisa has a total of fifty-four nickels and dimes. If shehad three more nickels, the value of the coins would be$4. How many of each does she have?Answer: 31 nickels; 23 dimes. n d 545(n 3) 10d 400 or 5n 10d 400 15 24. Algebra 2 WARM-UP 24 WORD PROBLEM WARM-UP 1Amy has two more nickels than dimes and five moredimes than quarters. Her nickels, dimes, and quarterstotal $3.25. How many of each kind does she have?Answer: 13 nickels; 11 dimes; 6 quarters.n d 2d q 5 5n 10d 25q 325 25. Algebra 2 WARM-UP 25 WORD PROBLEM WARM-UP 1Luke has three times as many nickels as dimes and fivetimes as many pennies as nickels. He has $2.80. Howmany of each coin does he have?Answer: 105 pennies; 21 nickels; 7 dimes.n 3dp 5n p 5n 10d 280 26. Algebra 2 WARM-UP 26 WORD PROBLEM WARM-UP 1If Eustace had twice as many nickels and half as manyquarters, he would have 60 less. Suppose he now hassixteen nickels and quarters. How many of each kinddoes he have?Answer: 105 pennies; 21 nickels; 7 dimes.n 3dp 5n p 5n 10d 280 27. Algebra 2 WARM-UP 27 WORD PROBLEM WARM-UP 1A rectangle whose perimeter is fifty feet is five feetlonger than it is wide. What are its dimensions? What isits area?Answer: w = 10 ft; l = 15 ft; A = 150 square feet P 2w 2l P 2w 2(w 5) P 4w 10 28. Algebra 2WARM-UP 28 WORD PROBLEM WARM-UP 1You are given the formula A = bc.Rewrite the given equation to show the effect of eachstatement. If b is increased by 6 and c is a. decreased by 2, then A increases by 15. b. increased by 2, then A doubles.Answer:a. A 15 (b 6)(c 2) b. 2A (b 6)(c 2) 29. Algebra 2 WARM-UP 29WORD PROBLEM WARM-UP 1You are given the formula A = bc.What is the effect on A if a. b is doubled and c is unchanged? b. b is doubled and c is halved? c. b is tripled and c is doubled?Answer: a. A is doubled b. A is unchanged c. A is six times as much 30. Algebra 2 WARM-UP 30 WORD PROBLEM WARM-UP 1You are given the formula for the area of a rectangle,A = lw, where l and w are in feet. Rewrite the givenequation to show the effect of each statement. a.If the length increases by 5 feet and the widthis unchanged, then the area increases by 40square feet. b. The width is two-thirds of the length.Answer:a. A 40 (l 5)w 2 2 b. A l 3 31. Algebra 2 WARM-UP 31WORD PROBLEM WARM-UP 175% of the length of a rectangle and 20% of its widthare eliminated. How does the area of the resultingrectangle compare with the area of the originalrectangle?Answer: New area is 20% of original areaA lw(.25l )(.80w ) .2(lw ) .20A 32. Algebra 2WARM-UP 32WORD PROBLEM WARM-UP 1The width of a rectangle is 40 cm less than itsperimeter. The rectangles area is 102 sq. cm. What arethe rectangles dimensions?Answer: 6 cm by 17 cm P 2(l w ) w P 40 102 lw 33. Algebra 2 WARM-UP 33 WORD PROBLEM WARM-UP 1A rectangle is three centimeters longer than it is wide.If its length were to be decreased by two centimeters,its area would decrease by thirty square centimeters.What is its area?Answer: 270 square centimeters l w 3 A lwA 30 (l 2)w 34. Algebra 2 WARM-UP 34WORD PROBLEM WARM-UP 1Porter drove for 3 hours at 40 mph and for 2 hours at50 mph. What was her average speed during that time?Answer: 44 mphD rt sumof distancesaverage speed= sumof timesD 40(3); D 50(2) 1 2 35. Algebra 2 WARM-UP 35WORD PROBLEM WARM-UP 1A car traveled from A to B at 50 mph, from B to C at 60mph, and returned (C to B to A) at 80 mph. What wasthe average speed on the round trip if the distancefrom A to B is 100 miles and from B to C is 120 miles?Answer: 65 5 mph27sumofdistances a average speed= sumof timesD D 2(D D ) a1 ; a 2 12t t 1 2 t t t 1 2 3 36. Algebra 2 WARM-UP 36 WORD PROBLEM WARM-UP 1It took 3 hours and 40 minutes for a car traveling at 60mph to go from A to B.a) How long will the return trip take if the car travels at 80 mph?b) What must the cars average speed be from B to A if the return trip is to be made in 2-1/2 hours?Answer: 2.75 hoursD = 60 x 3-2/3 = 220 mil