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P 2014 lesson 1 2014 01-03

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Adrian Ng
Adrian Ng

The document contained multiple math word problems involving quantities, ratios, money, ages, and rates of change over time. Each problem provided the relevant information, set up algebraic expressions or diagrams to represent the relationships, and solved for the unknown value being asked for through calculations.

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A farmer had a twice as many chicken as ducks. After he had sold 200 chickens, he had thrice as many ducks as chickens. How many chickens did he have at first? Ans.: 240 chicken ducks 2u x 3 = 6u 1u x 3 = 3u -200 x 6u – 1u --> 200 5u --> 200 1u --> 200 ÷ 5 = 40 6u --> 6 x 40 = 240 (ans.) 1u 3u
Jane and Ivan had $60. After giving Ivan $8, Jane had the same amount of money as Ivan. How much money did Ivan have at first? Ans.: $22 -8 Jane 1u 60 60 Ivan ? +8 2u --> 60 1u --> 60 ÷ 2 = 30 30 - 8 = 22 (ans.) 1u (30)
Thomas is 4 times as old as Sandra. Thomas will be twice as old as Sandra in 8 years time. How old is Thomas now? Ans.:16 Thomas Sandra +8 4u 1u 3u +8 6u – 4u --> 8 2u --> 8 1u --> 8 ÷ 2 = 4 Thomas (now): 4u --> 4 x 4 = 16 (ans.) 2u x 3 =6u 1u x 3 =3u 1u x3 =3u
John and Ramesh had an equal amount of sweets at first. John bought another 6 sweets and Ramesh lost 12 of her sweets. John had thrice as many sweets as Ramesh. Find the number of sweets each of them have first? Ans.:21 3u John Ramesh 6 1u 12 3u – 1u --> 12+ 6 2u --> 18 1u --> 18 ÷ 2 = 9 Each (1st): 1u + 12 --> 9 +12 = 21 (ans.)
Some children were sharing oranges. If each child took 3 oranges, there would be 2 left over. But if each child took 4 oranges, there would be 2 oranges short. How many oranges were there? Ans.:14 Total 3 each (12) 2 2 4 each 4 each – 3 each --> 2 + 2 1 each --> 4 3 each --> 3 x 4 = 12 Total: 12 + 2 = 14 (ans.)
A moment ago, Wendy had 2/5 as much money as Mike. Wendy withdrew $50 from her bank account. Now Wendy has 1/2 as much money as Mike. (a) How much money does Wendy have now? Ans.:$250 (b) What was the total amount of money the two of them had a moment ago? Ans.: $700 Wendy Mike 2u x 2 = 4u +50 5u x 2 = 10u x 1u x 5 = 5u 2u x 5 = 10u 5u – 4u --> 50 1u --> 50 Wendy (now) 5u --> 5 x 50 = 250 (ans.) Total (Before): 4u + 10 u = 14u 14u --> 14 x 50 = 700 (ans.)
Alex and his sister, Amber have a total of 120 computer games. If Alex gives Amber 5 games, Amber will have nine times as many games as Alex. How many more games does Amber have than Alex? Ans.: 86 Alex ? 17 -5 1u 120 120 Amber 103 +5 1u + 9u --> 120 10u --> 120 1u --> 120 ÷ 10 = 12 Alex (1st): 1u + 5 = 12 +5 = 17 120 – 17 = 103 103 – 17 = 86 (ans.) 9u
Olivia's mother was 4 times Olivia age 4 years ago. If their total age now is 48, how old is Olivia now? Ans.:12 4 years ago 48 – 4 – 4 = 40 mother Olivia 4u 1u now +4 +4 4u + 1u --> 40 5u --> 40 1u --> 40 ÷ 5 = 8 Olivia (Now): 1u + 4 = 8 +4 = 12 (ans.) 48
A moment ago, 84 pears and 65 apples were displayed at a fruit stall. 28 pears were sold and some more apples were displayed. Now, 5 times as many apples as pears are displayed. How many apples have just been displayed? Ans.:215 A moment ago pears apples 84 65 Now -28 +? 1u --> 84 – 28 = 56 5u --> 5 x 56 = 280 ?: 280 – 65 = 215 (ans.) 1u 5u (280)
Mrs. Tay has a bag of sweets. If she gives each child 7 sweets, she will be left with 5 sweets. If she gives each child 9 sweets, she will need 5 more sweets. a) How many children are there? Ans.:5 b) How many sweets are there? Ans.:40 Total 7 each (35) 5 5 9 each 9 each – 7each --> 5 + 5 2 each --> 10 1 each --> 10 ÷ 2 = 5 (a) 7 each --> 7 x 5 = 35 Total: 35 + 5 = 40 (b)
Jason and Kevin were given some money each. If Jason and Kevin spent $100 and $50 each day respectively, Jason would have $1300 when Kevin had spent all his money. If Jason and Kevin spent $50 and $100 each day respectively, Jason would have $3700 when Kevin spent all his money. How much money was given to Jason in the beginning? Ans.:$4500 Jason Kevin 100u 1300 -100 u -50 u 50u 1300 0 75u Jason Kevin 100u 50u 1300 -50 p ÷2 -25u -100 p ÷2 -50u 1300 3700 0 75u --> 3700 – 1300 = 2400 1u --> 2400 ÷ 75 = 32 Jason (1st): 100u + 1300 --> 100 x 32 + 1300 = 4500 (ans.)
Joe has 60% more marbles than Fred. First, Joe gave 20% of his marbles to Fred. In return, Fred gave 1/6 of his marbles to Joe. Finally, Fred had 80 fewer marbles than Joe. How many marbles did Joe have at first? Ans.:320 3/5 1/5 Joe 8u x 5 = 40u -8u Fred 5u x 5 = 25u +8u 32u 33u 10u --> 80 1u --> 80 ÷ 10 = 8 40u --> 40 x 8 = 320 (ans.) +5.5u -1/6 -5.5u 8/40 37.5u 27.5u 80 10u
When Mr Wong was Meimei's present age, she was 3 years old. When Meimei is Mr Wong's present age, he will be 81 years old. a) How much older is Mr Wong than Meimei? Ans.:26 b) How old is Mr Wong now? Ans.:55 Was Wong Meimei's 3 3 Present 1u 3 1u 3 Future 2u 1u 81 1u 3 2u 1u 2u + 1u --> 81 - 3 3u --> 78 1u --> 78 ÷ 3 = 26 (a) Wong (Now): 3 +2u --> 3 + 2 x 26 = 55 (b)
Alex and Betty each had $600 at first. Alex spent $6 per day and Betty spent $2 per day. How long did it take for Betty's money to be twice as much as Alex's money? Ans.:60 days Alex Betty -6 u 600 600 -2 u x2 1p --> 600 – 6u 2p --> 1200 – 12u 1p 2p 2p --> 600 – 2u 1200 2p 12u 2p 2u 600 12u – 2u -->1200 – 600 10u --> 600 1u --> 600 ÷ 10 = 60 (ans.)
If Eddie uses his money to buy 7 similar bags, he will have $5 more than Alice. If Alice uses some of her money to buy same 7 bags, she will have $47 less than Eddie. a) Find the cost of 1 bag. Ans.:$3 b) How much more money does Eddie have than Alice? Ans.:$26 ? Eddie 7 bags $5 Alice 7 bags $47 7 bags + 7 bags --> 47 - 5 14 bags --> 42 1 bag --> 42 ÷ 14 = 3 (a) 7 bags --> 7 x 3 = 21 21 + 5 = 26 (b)
Mr Tan had some apples and oranges in the ratio 4:5. After selling 170 apples and 25% of the oranges, the ratio of the apples to oranges left became 1:2. What was the number of fruits Mr Tan had in the end ? Ans.:450 1/4 5/20 apples oranges 4u x 4 = 16u 5u x 4 = 20u -170 1p x 7.5 = 7.5u -5u 16u – 7.5u --> 170 8.5u --> 170 1u --> 170 ÷ 8.5 = 20 Total (end): 7.5u + 15u = 22.5u 22.5u --> 22.5 x 20 = 450 (ans.) 15u 2p x 7.5 = 15u
Box A contained 350 black marbles and 500 white marbles. Box B contained 400 black marbles and 100 white marbles. After some black and white marbles were removed from Box B to be placed in Box A, 1/2 of the marbles in Box A were black and 3/4 of the marbles in Box B were black. a) How many black marbles were removed from Box B to be placed in Box A? Ans.:175 b) How many white marbles were removed from Box B to be placed in Box A? Ans.:25 Box A black white +? 350 Box B -? 1u +? 500 1u 1u + 1p --> 500 + 100 1u + 1p --> 600 1u --> 600 – 1p 1u + 3p --> 350 + 400 1u + 3p --> 750 1u --> 750 – 3p 750 1u 1u 600 3p 1p 3p – 1p --> 750 - 600 2p --> 150 400 100 -? (225) 3p 1p (75) 1p --> 150 ÷ 2 = 75 3p --> 3 x 75 = 225 400 - 225 = 175 (a) 100 - 75 = 25 (b)
When Kok's age was twice as Bala's age, Mike's age was 30. When Mike's age was twice Kok's age, Bala's age was 21. Given that Mike was the oldest among the three persons, find Bala's age when Mike was 62 years old. Ans.:35 Mike‘s Kok‘s Bala‘s 2p 30 2u 1u 1u 1u 1p 1p 21 21 2u + 1u --> 30 - 21 3u --> 9 1u --> 9 ÷ 3 = 3 62 (1u + 21) 1u ? 2u + 21 --> 2 x 3 + 21 = 27 62 – 27 = 35 (ans.) 2u + 21 (27)
Jane and Iris has 255 sweets altogether. Jane had 15 more sweets than Iris. Jane gave away 25% as many sweets as Iris. She was left with twice as many sweets as Iris. a) How many sweets did Iris give away? Ans.:60 1/4 b) How many sweets did Jane have in the end? Ans.:120 Jane 255 Iris -1u 135 15 120 -4u 2p 1p Iris: (255 – 15) ÷2 = 120 Jane: 120 + 15 = 135 2p --> 135 – 1u x2 1p --> 120 – 4u 2p --> 240 – 8u 240 2p 2p 135 8u 1u 8u – 1u --> 240 - 135 7u --> 105 1u --> 105 ÷ 7 = 15 Iris (gave): 4u --> 4 x 15 = 60 (a) Jane (end): 135 – 1u --> 135 – 15 = 120 (b)
If I buy 3 Oranges and 5 Apples, I will have $0.70 left. If I buy 4 oranges and 4 apples, I will need another $0.50. Given that an apple costs $0.80, find the amount of money I have. Ans.:$10.70 $4 $3.20 Total 3 OR $4 4 OR $0.70 $0.50 $3.20 4 OR – 3 OR --> 4 + 0.70 + 0.50 – 3.20 1OR --> 2 Total: 3 OR + 4 + 0.70 --> 3 x 2 + 4.70 = $10.70 (ans.)

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P 2014 lesson 1 2014 01-03

  • 1. A farmer had a twice as many chicken as ducks. After he had sold 200 chickens, he had thrice as many ducks as chickens. How many chickens did he have at first? Ans.: 240 chicken ducks 2u x 3 = 6u 1u x 3 = 3u -200 x 6u – 1u --> 200 5u --> 200 1u --> 200 ÷ 5 = 40 6u --> 6 x 40 = 240 (ans.) 1u 3u
  • 2. Jane and Ivan had $60. After giving Ivan $8, Jane had the same amount of money as Ivan. How much money did Ivan have at first? Ans.: $22 -8 Jane 1u 60 60 Ivan ? +8 2u --> 60 1u --> 60 ÷ 2 = 30 30 - 8 = 22 (ans.) 1u (30)
  • 3. Thomas is 4 times as old as Sandra. Thomas will be twice as old as Sandra in 8 years time. How old is Thomas now? Ans.:16 Thomas Sandra +8 4u 1u 3u +8 6u – 4u --> 8 2u --> 8 1u --> 8 ÷ 2 = 4 Thomas (now): 4u --> 4 x 4 = 16 (ans.) 2u x 3 =6u 1u x 3 =3u 1u x3 =3u
  • 4. John and Ramesh had an equal amount of sweets at first. John bought another 6 sweets and Ramesh lost 12 of her sweets. John had thrice as many sweets as Ramesh. Find the number of sweets each of them have first? Ans.:21 3u John Ramesh 6 1u 12 3u – 1u --> 12+ 6 2u --> 18 1u --> 18 ÷ 2 = 9 Each (1st): 1u + 12 --> 9 +12 = 21 (ans.)
  • 5. Some children were sharing oranges. If each child took 3 oranges, there would be 2 left over. But if each child took 4 oranges, there would be 2 oranges short. How many oranges were there? Ans.:14 Total 3 each (12) 2 2 4 each 4 each – 3 each --> 2 + 2 1 each --> 4 3 each --> 3 x 4 = 12 Total: 12 + 2 = 14 (ans.)
  • 6. A moment ago, Wendy had 2/5 as much money as Mike. Wendy withdrew $50 from her bank account. Now Wendy has 1/2 as much money as Mike. (a) How much money does Wendy have now? Ans.:$250 (b) What was the total amount of money the two of them had a moment ago? Ans.: $700 Wendy Mike 2u x 2 = 4u +50 5u x 2 = 10u x 1u x 5 = 5u 2u x 5 = 10u 5u – 4u --> 50 1u --> 50 Wendy (now) 5u --> 5 x 50 = 250 (ans.) Total (Before): 4u + 10 u = 14u 14u --> 14 x 50 = 700 (ans.)
  • 7. Alex and his sister, Amber have a total of 120 computer games. If Alex gives Amber 5 games, Amber will have nine times as many games as Alex. How many more games does Amber have than Alex? Ans.: 86 Alex ? 17 -5 1u 120 120 Amber 103 +5 1u + 9u --> 120 10u --> 120 1u --> 120 ÷ 10 = 12 Alex (1st): 1u + 5 = 12 +5 = 17 120 – 17 = 103 103 – 17 = 86 (ans.) 9u
  • 8. Olivia's mother was 4 times Olivia age 4 years ago. If their total age now is 48, how old is Olivia now? Ans.:12 4 years ago 48 – 4 – 4 = 40 mother Olivia 4u 1u now +4 +4 4u + 1u --> 40 5u --> 40 1u --> 40 ÷ 5 = 8 Olivia (Now): 1u + 4 = 8 +4 = 12 (ans.) 48
  • 9. A moment ago, 84 pears and 65 apples were displayed at a fruit stall. 28 pears were sold and some more apples were displayed. Now, 5 times as many apples as pears are displayed. How many apples have just been displayed? Ans.:215 A moment ago pears apples 84 65 Now -28 +? 1u --> 84 – 28 = 56 5u --> 5 x 56 = 280 ?: 280 – 65 = 215 (ans.) 1u 5u (280)
  • 10. Mrs. Tay has a bag of sweets. If she gives each child 7 sweets, she will be left with 5 sweets. If she gives each child 9 sweets, she will need 5 more sweets. a) How many children are there? Ans.:5 b) How many sweets are there? Ans.:40 Total 7 each (35) 5 5 9 each 9 each – 7each --> 5 + 5 2 each --> 10 1 each --> 10 ÷ 2 = 5 (a) 7 each --> 7 x 5 = 35 Total: 35 + 5 = 40 (b)
  • 11. Jason and Kevin were given some money each. If Jason and Kevin spent $100 and $50 each day respectively, Jason would have $1300 when Kevin had spent all his money. If Jason and Kevin spent $50 and $100 each day respectively, Jason would have $3700 when Kevin spent all his money. How much money was given to Jason in the beginning? Ans.:$4500 Jason Kevin 100u 1300 -100 u -50 u 50u 1300 0 75u Jason Kevin 100u 50u 1300 -50 p ÷2 -25u -100 p ÷2 -50u 1300 3700 0 75u --> 3700 – 1300 = 2400 1u --> 2400 ÷ 75 = 32 Jason (1st): 100u + 1300 --> 100 x 32 + 1300 = 4500 (ans.)
  • 12. Joe has 60% more marbles than Fred. First, Joe gave 20% of his marbles to Fred. In return, Fred gave 1/6 of his marbles to Joe. Finally, Fred had 80 fewer marbles than Joe. How many marbles did Joe have at first? Ans.:320 3/5 1/5 Joe 8u x 5 = 40u -8u Fred 5u x 5 = 25u +8u 32u 33u 10u --> 80 1u --> 80 ÷ 10 = 8 40u --> 40 x 8 = 320 (ans.) +5.5u -1/6 -5.5u 8/40 37.5u 27.5u 80 10u
  • 13. When Mr Wong was Meimei's present age, she was 3 years old. When Meimei is Mr Wong's present age, he will be 81 years old. a) How much older is Mr Wong than Meimei? Ans.:26 b) How old is Mr Wong now? Ans.:55 Was Wong Meimei's 3 3 Present 1u 3 1u 3 Future 2u 1u 81 1u 3 2u 1u 2u + 1u --> 81 - 3 3u --> 78 1u --> 78 ÷ 3 = 26 (a) Wong (Now): 3 +2u --> 3 + 2 x 26 = 55 (b)
  • 14. Alex and Betty each had $600 at first. Alex spent $6 per day and Betty spent $2 per day. How long did it take for Betty's money to be twice as much as Alex's money? Ans.:60 days Alex Betty -6 u 600 600 -2 u x2 1p --> 600 – 6u 2p --> 1200 – 12u 1p 2p 2p --> 600 – 2u 1200 2p 12u 2p 2u 600 12u – 2u -->1200 – 600 10u --> 600 1u --> 600 ÷ 10 = 60 (ans.)
  • 15. If Eddie uses his money to buy 7 similar bags, he will have $5 more than Alice. If Alice uses some of her money to buy same 7 bags, she will have $47 less than Eddie. a) Find the cost of 1 bag. Ans.:$3 b) How much more money does Eddie have than Alice? Ans.:$26 ? Eddie 7 bags $5 Alice 7 bags $47 7 bags + 7 bags --> 47 - 5 14 bags --> 42 1 bag --> 42 ÷ 14 = 3 (a) 7 bags --> 7 x 3 = 21 21 + 5 = 26 (b)
  • 16. Mr Tan had some apples and oranges in the ratio 4:5. After selling 170 apples and 25% of the oranges, the ratio of the apples to oranges left became 1:2. What was the number of fruits Mr Tan had in the end ? Ans.:450 1/4 5/20 apples oranges 4u x 4 = 16u 5u x 4 = 20u -170 1p x 7.5 = 7.5u -5u 16u – 7.5u --> 170 8.5u --> 170 1u --> 170 ÷ 8.5 = 20 Total (end): 7.5u + 15u = 22.5u 22.5u --> 22.5 x 20 = 450 (ans.) 15u 2p x 7.5 = 15u
  • 17. Box A contained 350 black marbles and 500 white marbles. Box B contained 400 black marbles and 100 white marbles. After some black and white marbles were removed from Box B to be placed in Box A, 1/2 of the marbles in Box A were black and 3/4 of the marbles in Box B were black. a) How many black marbles were removed from Box B to be placed in Box A? Ans.:175 b) How many white marbles were removed from Box B to be placed in Box A? Ans.:25 Box A black white +? 350 Box B -? 1u +? 500 1u 1u + 1p --> 500 + 100 1u + 1p --> 600 1u --> 600 – 1p 1u + 3p --> 350 + 400 1u + 3p --> 750 1u --> 750 – 3p 750 1u 1u 600 3p 1p 3p – 1p --> 750 - 600 2p --> 150 400 100 -? (225) 3p 1p (75) 1p --> 150 ÷ 2 = 75 3p --> 3 x 75 = 225 400 - 225 = 175 (a) 100 - 75 = 25 (b)
  • 18. When Kok's age was twice as Bala's age, Mike's age was 30. When Mike's age was twice Kok's age, Bala's age was 21. Given that Mike was the oldest among the three persons, find Bala's age when Mike was 62 years old. Ans.:35 Mike‘s Kok‘s Bala‘s 2p 30 2u 1u 1u 1u 1p 1p 21 21 2u + 1u --> 30 - 21 3u --> 9 1u --> 9 ÷ 3 = 3 62 (1u + 21) 1u ? 2u + 21 --> 2 x 3 + 21 = 27 62 – 27 = 35 (ans.) 2u + 21 (27)
  • 19. Jane and Iris has 255 sweets altogether. Jane had 15 more sweets than Iris. Jane gave away 25% as many sweets as Iris. She was left with twice as many sweets as Iris. a) How many sweets did Iris give away? Ans.:60 1/4 b) How many sweets did Jane have in the end? Ans.:120 Jane 255 Iris -1u 135 15 120 -4u 2p 1p Iris: (255 – 15) ÷2 = 120 Jane: 120 + 15 = 135 2p --> 135 – 1u x2 1p --> 120 – 4u 2p --> 240 – 8u 240 2p 2p 135 8u 1u 8u – 1u --> 240 - 135 7u --> 105 1u --> 105 ÷ 7 = 15 Iris (gave): 4u --> 4 x 15 = 60 (a) Jane (end): 135 – 1u --> 135 – 15 = 120 (b)
  • 20. If I buy 3 Oranges and 5 Apples, I will have $0.70 left. If I buy 4 oranges and 4 apples, I will need another $0.50. Given that an apple costs $0.80, find the amount of money I have. Ans.:$10.70 $4 $3.20 Total 3 OR $4 4 OR $0.70 $0.50 $3.20 4 OR – 3 OR --> 4 + 0.70 + 0.50 – 3.20 1OR --> 2 Total: 3 OR + 4 + 0.70 --> 3 x 2 + 4.70 = $10.70 (ans.)