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Slide 3 Slide 33 Slide 48 Slide 75 Slide 90 Slide 98 Table of Contents Basic Number Problems Number and Money Problems Age and Digit Problems Mixture Problems.

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Presentation on theme: "Slide 3 Slide 33 Slide 48 Slide 75 Slide 90 Slide 98 Table of Contents Basic Number Problems Number and Money Problems Age and Digit Problems Mixture Problems."— Presentation transcript:

1 Slide 3 Slide 33 Slide 48 Slide 75 Slide 90 Slide 98 Table of Contents Basic Number Problems Number and Money Problems Age and Digit Problems Mixture Problems Motion (D=RT) Problems Test Review Problems Test Review

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3 Systems of Equations chapter 6 Word Problems: Money

4 1 taco 1 milk Total $2.10 1 taco 1 milk Total $2.10 2 taco 3 milk Total $5.15 2 taco 3 milk Total $5.15 Find the cost of a taco Ex #1 Define variables :

5 1 taco 1 milk Total $2.10 1 taco 1 milk Total $2.10 2 taco 3 milk Total $5.15 2 taco 3 milk Total $5.15 Ex #1 Write two equations : Find the cost of a taco

6 Solve the system Ex #1

7 1 taco 1 milk Total $2.10 1 taco 1 milk Total $2.10 2 taco 3 milk Total $5.15 2 taco 3 milk Total $5.15 Ex #1 Find the cost of a taco

8 Four Oranges and five apples cost $3.56. Three oranges and four apples cost $2.76. Find the cost of an orange. Define variables : Let r be the cost of an orange Write two equations E1 E2 Solve the system An orange is $0.44 Let a be the cost of an Apple #2

9 A jar of dimes and quarters contains $15.25. There are 103 coins in all. How many quarters are in the jar? Ex. #3 Define variables :

10 A jar of dimes and quarters contains $15.25. There are 103 coins in all. How many quarters are in the jar? Ex. #3 Define variables : Write two equations E1 E2

11 A jar of dimes and quarters contains $15.25. There are 103 coins in all. How many quarters are in the jar? Ex. #3 Define variables :

12 Combined, Peyton and Eli have $106.75. Peyton has $43.75 more than Eli. How much money does Peyton have? Ex. #4 Define variables : Write two equations E1 E2

13 #1 At a football game, a popcorn and a soda purchased together costs $4.00. Three popcorns and five sodas would cost $16.50. What is the cost of a single soda? Define variables p Let p be the cost of a popcorn Let s be the cost of a soda Write two equations E1 E2

14 #1 At a football game, a popcorn and a soda purchased together costs $4.00. Three popcorns and five sodas would cost $16.50. What is the cost of a single soda? p Let p be the cost of a popcorn Let s be the cost of a soda E1 E2

15 #2 Four apples and five bananas cost $3.75. Six apples and two bananas cost $2.82. What is the cost of a single banana? Define variables a Let a be the cost of 1 apple Let b be the cost of 1 banana Write two equations E1 E2

16 #2 Four apples and five bananas cost $3.75. Six apples and two bananas cost $2.82. What is the cost of a single banana? a Let a be the cost of 1 apple Let b be the cost of 1 banana

17 #3 Define variables : d Let d be the number of dimes Let q be the number of quarters Write two equations A vending machine takes only dimes and quarters. There are 113 coins in the machine totaling $17.60. How many quarters are in the machine? E1 E2

18 #3 A vending machine takes only dimes and quarters. There are 113 coins in the machine totaling $17.60. How many quarters are in the machine? d Let d be the number of dimes Let q be the number of quarters

19 #4 There are 40 coins in Jennys coin purse – all dimes and nickels. All together it adds to $2.65. How many nickels are in Jennys purse? Define variables : d Let d be the number of dimes Let n be the number of nickels Write two equations

20 #4 There are 40 coins in Jennys coin purse – all dimes and nickels. All together it adds to $2.65. How many nickels are in Jennys purse? d Let d be the number of dimes Let n be the number of nickels

21 #5 Combined, Bart and Lisa have $62.75. Lisa has $13.75 more than Bart. How much money does Bart have? L Let L be Lisas money Let B be Barts money Define variables : Write two equations

22 #6 Otis has three times as much money as Milo. Together they have $60.84. How much money does each one of them have? t Let t be Otis money Let m be Milos money

23 Systems of Equations chapter 6 Basic Word Problems:

24 Example 1 The sum of two numbers is 49. One number is 13 less than the other. Find the numbers. Define variables : Let x be the larger number Let y be the smaller number Write two equations E1 E2 Solve the system

25 The difference between two numbers is 16. Three times the larger number is seven times the smaller. What are the numbers? Define variables : Let x be the larger number Let y be the smaller number Write two equations E1 E2 Example 2

26 The sum of a number and twice another number is 13. The first number is 4 larger than the second number. What are the two numbers? Define variables : Let x xx x be the first number (larger) Let y yy y be the second number Write two equations E1 E2 Solve the system Example 3

27 #3 The sum of two numbers is 82. One number is 12 more than the other. Find the larger number. Define variables : Let L be the larger number Let S be the smaller number Write two equations E1 E2

28 #3 The sum of two numbers is 82. One number is 12 more than the other. Find the larger number. Define variables : Let L be the larger number Let S be the smaller number Write two equations E1 E2

29 #3 The sum of two numbers is 82. One number is 12 more than the other. Find the larger number. Define variables : Let L be the larger number Let S be the smaller number Write two equations E1 E2 Solve the system

30 #4 The difference between two numbers is 6. Ten times the smaller number is six times the larger. Find the numbers. Define variables : Let L be the larger number Let S be the smaller number Write two equations E1 E2 Solve the system

31 #5 The sum of a number and twice another number is 37. The first number is 10 larger than the second number. What are the two numbers? Define variables : Let L be the larger number Let S be the smaller number Write two equations E1 E2 Solve the system

32 The product of 4 times the sum of a number and 3 is another number. If the sum of the numbers is 67, what is the smallest of the two numbers? Define variables : Let x be one number Let y be the other number Write two equations E1 E2 Solve the system #6

33 Systems of Equations chapter 6 More Word Problems:

34 #1 Farmer Bob had 25 animals in the barn – all of them either cows or chickens. He counted 66 legs in all. How many cows are in the barn?

35 The price of a ticket for the AVHS basketball game is $2.75 for a student, but only $2.25 if you have a discount card. One ticket taker sold 59 tickets for $141.75. How many students didnt use a discount card? x Let x be the number of students w/o discount cards Let y be the number of students with discount cards #2

36 #3 At Randys bike shop, they only work on bicycles and tricycles. When Randy disassembled all the bikes and trikes he ended up with 34 seats and 89 wheels. How many tricycles does he have in his shop?

37 #4 Sydney took a math test that had 32 questions on it and scored 111 points. Each correct answer was awarded 5 points and for each wrong answer two points were deducted. How many questions did she miss on her test?

38 #5 Will set a school record by scoring 30 points in his basketball game. What was amazing is that he scored all his points without a single free-throw. Out of the 13 baskets that he made, how many were 3-point shots?

39 #6 Jackies coin purse had only dimes and quarters in it. There were 5 more dimes than quarters, and the total amount of money was $7.85. How many dimes were in the purse?

40 #7 x Let x be the number of T/F questions Let y be the number of other questions A science test has 25 questions on it and is worth a total of 66 points. The true/false questions are worth 2 points each and the rest of the questions are worth 3 points each. How many true/false questions are on the test?

41 #8 At a movie theater, tickets cost $9.50 for adults and $6.50 for children. A group of 7 moviegoers pays a total of $54.50. How many adults are in the group? a Let a be the number of adults Let c be the number of children

42 #1 At the baseball game field level seats cost $9.50 each, while seats in the second deck cost $6.25. If a ticket seller sold 52 tickets and collected $425.75, how many second deck seats did she sell? f Let f be the number of field level tickets. Let s be the number of 2 nd deck tickets.

43 #4 A History test has 40 questions on it and is worth a total of 174 points. The true/false questions are worth 3 points each and the rest of the questions are worth 5 points each. How many true/false questions are on the test?

44 #6 A jar contains quarters and dimes. There are 15 more quarters than dimes. The total amount of money in the jar is $23. How many quarters are in the jar?

45 #7 At the coffee shop, two bagels and three muffins cost $12.45. Three bagels and five muffins cost $20.00. What is the cost of a single bagel? Let b be the cost of a bagel E1 E2 Let m be the cost of a muffin

46 #10 The sum of two integers is 35 and the difference between the same two integers is 81. What is the smaller integer? Let L be the larger number Let S be the smaller number E1 E2

47 Haley was going to be paid to unpack a box of 125 delicate crystal ornaments. She would be paid 75 cents for each ornament unpacked, but would be charged $2.50 for any that she broke. After finishing the job she was paid $74.25. How many ornaments did she break? x Let x be the number of ornaments unpacked successfully. Let y be the number of ornaments broken #9- Bonus

48 Systems of Equations chapter 6 Basic Word Problems: Age Age Number-Digit Number-Digit

49 #1 The sum of the digits of a two-digit number is 10. When the digits are reversed, the new number is 54 more than the original number. What is the original number? Let t be the tens digit of the original number Let u be the units (ones) digit of the original number E1: E2: Original number New number

50 #2 The sum of the digits of a two-digit number is 7. When the digits are reversed, the new number is 45 less than the original number. What is the original number? Let t be the tens digit of the original number Let u be the units (ones) digit of the original number E1: E2: Original number New number

51 Andy is 21 years older than Bob. In two years, Andy will be twice as old as Bob. What is Andys current age? Let a be Andys current age Let b be Bobs current age Ex. 3 Age in 2 years E1: E2:

52 Andy is 21 years older than Bob. In two years, Andy will be twice as old as Bob. What is Andys current age? Let a be Andys current age Let b be Bobs current age Ex. 3 Age in 2 years E1: E2:

53 #4 Tom is 5 years older than Jerry. Last year Tom was twice as old as Jerry. How old is Tom today? Let t be Toms current age Let j be Jerrys current age Last year E1: E2:

54 #4 Tom is 5 years older than Jerry. Last year Tom was twice as old as Jerry. How old is Tom today? Let t be Toms current age Let j be Jerrys current age Last year E1: E2:

55 #9 x Let x be the cost of an adult ticket Let y be the cost of a youth ticket E1 E2

56 #10 x Let x be the number of Granny Smith apples Let y be the number of Gala apples

57 Let a be the measure of angle a Let b be the measure of angle b E1 E2 #2#2 Angle a and angle b are complementary angles. The measure of angle b is 12 more than twice the measure of angle a. Find the measure of angle a.

58 #7 x Let x be the cost of an adult ticket Let y be the cost of a youth ticket E1 E2

59 #8 x Let x be the number of Granny Smith apples Let y be the number of Gala apples

60 #1#1 #2#2 Marcus is 5 years older than Katie. Last year he was twice as old as she was. How old will Katie be next year? Angle a and angle b are complementary angles. The measure of angle b is 12 more than twice the measure of angle a. Find the measure of angle a.

61 #1#1 Marcus is 5 years older than Katie. Last year he was twice as old as she was. How old will Katie be next year? Let m be Marcuss current age Let k be Katies current age Age last year E1: E2:

62 #1#1 Marcus is 5 years older than Katie. Last year he was twice as old as she was. How old will Katie be next year? Let m be Marcuss current age Let k be Katies current age Age last year E1: E2:

63 Let a be the measure of angle a Let b be the measure of angle b E1 E2 #2#2 Angle a and angle b are complementary angles. The measure of angle b is 12 more than twice the measure of angle a. Find the measure of angle a.

64 #1 A cashier is counting money at the end of the day. She has a stack that contains only $5 bills and $10 bills. There are 45 bills in the stack for a total of $290. How many $5 bills are in the stack?

65 #2 The sum of the digits of a two-digit number is 13. When the digits are reversed the new number is 27 more than the original number. What was the original number? Let t be the tens digit of the original number Let u be the units (ones) digit of the original number E1: E2: Original numberNew number

66 Let d be Danielles current age Let a be Alisons current age #3 Age 2 years ago E1: E2: Danielle is 36 years older than her daughter Alison. Two years ago, Danielle was 5 times as old as Alison. Find Alisons current age.

67 Let d be Danielles current age Let a be Alisons current age #3 Age in 2 years E1: E2: Danielle is 36 years older than her daughter Alison. Two years ago, Danielle was 5 times as old as Alison. Find Alisons current age.

68 A jar contains 55 quarters and dimes. The total amount of money in the jar is $8.50. Find the number of dimes in the jar #4

69 #5 Becky is selling tickets to a school play. Adult tickets cost $12 and student tickets cost $6. Becky sells a total of 48 tickets and collects a total of $336. How many $6 tickets did she sell? Let a be the number of adult tickets Let s be the number of student tickets E1: E2:

70 #6 The sum of the digits of a two-digit number is 14. The first digit is 4 less than twice the second digit. What is the number? Let t be the tens digit of the number Let u be the ones digit of the number E1: E2:

71 Five years ago, Beth was three times as old as Frank. Next year she will be twice as old as Frank. How old is Beth today? #7 b is Beths current age f is Franks current age Age 5 years ago E1: E2: Age next year

72 Five years ago, Beth was three times as old as Frank. Next year she will be twice as old as Frank. How old is Beth today? #7 b is Beths current age f is Franks current age Age 5 years ago E1: E2: Age next year

73 Five years ago, Beth was three times as old as Frank. Next year she will be twice as old as Frank. How old is Beth today? #7 b is Beths current age f is Franks current age Age 5 years ago E1: E2: Age next year

74 Angle a and angle b are complementary angles. Angle b is 15 more than four times angle a. Find the measure of both angles. #8 Let a be the measure of angle a Let b be the measure of angle b E1 E2

75 Systems of Equations chapter 6 Basic Word Problems: Mixture Problems Mixture Problems

76 a a = amount of 12% solution b b = amount of 20% solution A chemist mixes a 12% alcohol solution with a 20% alcohol solution to make 300 milliliters of an 18% alcohol solution. How many milliliters of each solution does the chemist use? 12% solution 18% solution 20% solution#1#1

77 Amount of Solution Amount of alcohol ab 300 + = 0.12a0.20b 0.18(300) = 54 54 12% solution 20% solution 18% solution A chemist mixes a 12% alcohol solution with a 20% alcohol solution to make 300 milliliters of an 18% alcohol solution. How many milliliters of each solution does the chemist use? #1#1 a a = amount of 12% solution b b = amount of 20% solution

78 Amount of Solution Amount of alcohol ab 300 + = 0.12x0.20y 0.18(300) = 54 54 12% solution 20% solution 18% solution A chemist mixes a 12% alcohol solution with a 20% alcohol solution to make 300 milliliters of an 18% alcohol solution. How many milliliters of each solution does the chemist use? #1#1 a a = amount of 12% solution b b = amount of 20% solution

79 Amount of Solution Amount of alcohol ab 300 + = 0.12x0.20y 0.18(300) = 54 54 12% solution 20% solution 18% solution A chemist mixes a 12% alcohol solution with a 20% alcohol solution to make 300 milliliters of an 18% alcohol solution. How many milliliters of each solution does the chemist use? #1#1 a a = amount of 12% solution b b = amount of 20% solution 75 milliliters of 12% solution 225 milliliters of 20% solution

80 a a = amount of 30% solution b b = amount of 50% solution A solution containing 30% insecticide is to be mixed with a solution containing 50% insecticide to make 200 Liters of a solution containing 42% insecticide. How much of each solution should be used? 0.42(200) = 84 #2#2 Amount of Solution Pure insecticide a b 200 0.3a0.5b 84 + = 30% solution 50% solution 42% solution

81 a a = amount of 30% solution b b = amount of 50% solution A solution containing 30% insecticide is to be mixed with a solution containing 50% insecticide to make 200 Liters of a solution containing 42% insecticide. How much of each solution should be used? #2#2 120 milliliters of 50% solution 80 milliliters of 30% solution

82 #3#3 c c = amount of Columbian beans (lbs.). h h = amount of Hawaiian beans (lbs.) Amount of Beans (lbs.) Cost of Beans ($) c h100 1.50c3.50h 270 + = Columbian Hawaiian Christmas Blend Starbucks wants to make 100 pounds of their special Christmas blend and sell it for $2.70 per pound. They will mix Columbian beans that sell for $1.50 per pound and Hawaiian beans that cost $3.50 per pound. How many pounds of the Hawaiian beans will they need to order?

83 #3#3 c c = amount of Columbian beans (lbs.). h h = amount of Hawaiian beans (lbs.) 60 pounds of Hawaiian beans

84 Amount of Solution Amount of Saline ab 800 + = 0.3a0.5b 0.45(800) = 360 360 30% solution 50% solution 45% solution Jenny mixes a 30% saline solution with a 50% saline solution to make 800 milliliters of a 45% saline solution. How many milliliters of each solution does she use? #1#1 a a = amount of 30% solution (ml) b b = amount of 50% solution (ml)

85 Jenny mixes a 30% saline solution with a 50% saline solution to make 800 milliliters of a 45% saline solution. How many milliliters of each solution does she use? #1#1 a a = amount of 30% solution (ml) b b = amount of 50% solution (ml) 200 milliliters of 30% solution 600 milliliters of 50% solution

86 Amount of mix Amount of aspirin ab 10 + = 0.10a0.25b 0.16(10) = 1.6 1.6 10% mix 25% mix 16% mix A pharmacist wants to mix medicine that is 10% aspirin with a medicine that is 25% aspirin to make 10 grams of a medicine that is 16% aspirin. How many grams of each medicine should the pharmacist mix together? #2#2 a a = amount of 10% mix (grams) b b = amount of 25% mix (grams)

87 A pharmacist wants to mix medicine that is 10% aspirin with a medicine that is 25% aspirin to make 10 grams of a medicine that is 16% aspirin. How many grams of each medicine should the pharmacist mix together? #2#2 a a = amount of 10% mix (grams) b b = amount of 25% mix (grams) 6 grams of 10% mix 4 grams of 25% mix

88 #3#3 p p = amount of peanuts (lbs.). r r = amount of raisins (lbs.) Weight of stuff (lbs.) Cost of stuff ($) p r 8 1.60p2.40r 17.60 + = Peanuts Raisins Mixture Peanuts cost $1.60 per pound and raisins cost $2.40 per pound. Brad wants to make 8 pounds of a mixture that costs $2.20 per pound. How many pounds of peanuts and raisins should he use? 8(2.20) = 17.60

89 #3#3 p p = amount of peanuts (lbs.). r r = amount of raisins (lbs.) Peanuts cost $1.60 per pound and raisins cost $2.40 per pound. Brad wants to make 8 pounds of a mixture that costs $2.20 per pound. How many pounds of peanuts and raisins should he use? 2 pounds of peanuts 6 pounds of raisins

90 Systems of Equations chapter 6 Basic Word Problems: Motion Problems Motion Problems

91 Motion Problems Motion problems involve distance, time and rate. The equation that links these concepts is called The Distance Formula: d = r t d = distance t = time r = rate miles miles kilometers kilometers meters meters feet feet inches inches hours hours minutes minutes seconds seconds days days years years miles/hour miles/hour km/min. km/min. m/s m/s ft./sec. ft./sec. inches/sec. inches/sec.

92 A jet airplane flies 2000 miles with the wind in four hours. The return trip against the same takes 5 hours. Find the speed of the jet and the speed of the wind. 11 Wind d = 2000 miles t = 4 hours

93 A jet airplane flies 2000 miles with the wind in four hours. The return trip against the same takes 5 hours. Find the speed of the jet and the speed of the wind. 11 Wind d = 2000 miles t = 4 hours d = 2000 miles t = 5 hours w = speed of wind j = speed of the jet

94 With the wind w = speed of wind 11 j = speed of the jet A jet airplane flies 2000 miles with the wind in four hours. The return trip against the same takes 5 hours. Find the speed of the jet and the speed of the wind. Against the wind

95 w = speed of wind 11 j = speed of the jet A jet airplane flies 2000 miles with the wind in four hours. The return trip against the same takes 5 hours. Find the speed of the jet and the speed of the wind. Speed of the jet = 450 mph Speed of the wind = 50 mph

96 With the current c = speed of the current (mph) 22 b = speed that Ben can paddle in still water (mph). Ben paddles his kayak 8 miles upstream in 4 hours. He turns around and paddles back downstream to his starting point in just 2 hours. What is the speed of the current? Against the current

97 c = speed of the current (mph) 22 b = speed that Ben can paddle in still water (mph). Ben paddles his kayak 8 miles upstream in 4 hours. He turns around and paddles back downstream to his starting point in just 2 hours. What is the speed of the current? Speed of current = 1 mph Speed that ben can paddle = 3 mph

98 Systems of Equations chapter 6 Test Review

99 With the wind w = speed of wind 11 c = speed of the helicopter With a tailwind, a helicopter flies 300 miles in 1.5 hours. When the helicopter flies back against the same wind, the trip takes 3 hours. What is the helicopters speed in still air? What is the speed of the wind? Against the wind

100 11 Speed of the heli. = 150 mph Speed of the wind = 50 mph w = speed of wind c = speed of the helicopter With a tailwind, a helicopter flies 300 miles in 1.5 hours. When the helicopter flies back against the same wind, the trip takes 3 hours. What is the helicopters speed in still air? What is the speed of the wind?

101 With the current c = speed of current 22 b = speed of the barge A barge on the Sacramento river travels 24 miles upstream in 3 hours. The return trip take the barge only two hours. Find the speed of the barge in still water. Against the current

102 Speed of the barge = 10 mph Speed of the current = 2 mph c = speed of current b = speed of the barge 22 A barge on the Sacramento river travels 24 miles upstream in 3 hours. The return trip take the barge only two hours. Find the speed of the barge in still water.

103 Amount of Solution Amount of Acid ab 500 + = 0.1a0.2b 0.16(500) = 80 80 10% solution 20% solution 16% solution A chemist mixes a 10% acid solution with a 20% acid solution to make 500 milliliters of a 16% acid solution. How much of the 20% solution did he use in his mixture? #3#3 a a = amount of 10% acid solution (ml) b b = amount of 20% acid solution (ml)

104 A chemist mixes a 10% acid solution with a 20% acid solution to make 500 milliliters of a 16% acid solution. How much of the 20% solution did he use in his mixture? #3#3 200 ml of 10% acid solution 300 ml of 20% acid solution a a = amount of 10% acid solution (ml) b b = amount of 20% acid solution (ml)

105 #4#4 a a = amount of apricots (lbs.). c c = amount of cherries (lbs.) Weight of stuff (lbs.) Cost of stuff ($) a c 20 1.50a3.50c 54 + = apricots cherries Mixture At the Snack Shack, dried cherries cost $3.50 per pound. Dried apricots cost $1.50 per pound. The stores owner wants to make 20 pounds of a mixture that costs $2.70 per pound. How many pounds of cherries will be needed to make the mixture? 20(2.70) = 54

106 #4#4 12 pounds of cherries At the Snack Shack, dried cherries cost $3.50 per pound. Dried apricots cost $1.50 per pound. The stores owner wants to make 20 pounds of a mixture that costs $2.70 per pound. How many pounds of cherries will be needed to make the mixture? a a = amount of apricots (lbs.). c c = amount of cherries (lbs.)

107 Are You Ready For The Test? Which system can solve the word problem given?

108 At the hardware store, 15 screws and 7 bolts weigh 303 grams. 12 bolts and 5 screws weigh 188 grams. What will 9 bolts weigh? b = weight of a bolt s = weight of a screw #1

109 Andy is 21 years older than Bob. In two years, Andy will be twice as old as Bob. What is Andys current age? Let a be Andys current age Let b be Bobs current age #2


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