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2019 Junior Algebra Equations L3&4 Practise.pdf2019 Junior Algebra Equations L3&4 Practise Answers.pdf • Find and justify a word formula which represents a given practical situation.
• Find and justify a word formula which represents a given practical situation.
We can solve these word problems using number skills:
- 42 heads, with two legs per head is 84 feet. We need 124 feet. 124-84=40 & 40/2=20. There must be 20 rabbits and 22 chickens.
- 34 heads with two legs per head is 68 feet. We need 114 feet. 114-68=44 & 44/2=22. There must be 11 donkeys and 23 children.
We can solve using simultaneous equations:
- This would be Level 5 OR Level 6 of the NZC.
- The working makes the Level shift from Level 4 to Level 5 or 6.
- Rabbits have 4 feet, so if "r" is the number of rabbits then 4r is the number of rabbit feet.
- Chickens have 2 feet, so it "c" is the number of chickens then 2c is the number of chicken feet.
- The total number of feet is 124
- 4r+2c=124
- Rabbits and Chickens have one head, so the number of rabbits plus the number of chickens equals 42.
- r+c=42
- Now we need to solve r+c=42 and 4r+2c=124
- We can rearrange r+c=42 to give c=42-r
- We can replace the "c" in "4r+2c=124" with "42-r"
- 4r+2(42-r)=124
- 4r+84-2r=124
- 2r=124-84
- 2r=40
- r=40/2
- r=20
- There are 20 Rabbits.
- c=42-r
- c=42-20
- c=22
- There are 22 Chickens.
- Check 22 Chickens plus 20 Rabbits = 42 Heads.
- Check 22 Chickens gives 44 feet and 20 Rabbits gives 80 Feet.
- 44+80=124 feet. Correct.
- Donkeys have 4 feet, so if "d" is the number of donkeys then 4d is the number of donkey feet.
- Children have 2 feet, so it "c" is the number of children then 2c is the number of children feet.
- The total number of feet is 114
- 4d+2c=114
- Donkeys and Children have one head, so the number of donkeys plus the number of children equals 34.
- d+c=34
- Now we need to solve d+c=34 and 4d+2c=114
- We can rearrange d+c=34 to give c=34-d
- We can replace the "c" in "4d+2c=114" with "34-d"
- 4d+2(34-d)=114
- 4d+68-2d=114
- 2d=114-68
- 2d=46
- d=46/2
- d=23
- There are 23 donkeys.
- c=34-d
- c=34-23
- c=11
- There are 11 children.
- Check 11 Children plus 23 Donkeys = 34 Heads.
- Check 11 Children gives 22 feet and 23 Donkeys gives 92 Feet.
- 22+92=124 feet. Correct.
- Let g represent the number of girls.
- Let b represent the number of boys.
- b+g=672
- 2g=b (There are twice as many boys as girls)
- 2g+g=672
- 3g=672
- g=672/3
- g=224 There are 224 Girls.
- b=2g
- b=448 There are 448 Boys.
- Check 448+224=672 Correct
• Solve simple linear equations that involve more than one step.
• Solve simple linear equations that involve more than one step.
• Solve simple linear inequalities that do not involve reversing the inequality sign.
• Solve simple linear inequalities that do not involve reversing the inequality sign.
Level 5
Level 5
• Form linear equations to model a given situation.
• Form linear equations to model a given situation.
• Solve linear equations that require multiple steps.
• Solve linear equations that require multiple steps.
• Solve linear equations that contain algebraic fractions.
• Solve linear equations that contain algebraic fractions.
• Use equations to represent practical situations.
• Use equations to represent practical situations.
- These are word problems.
- Use letters to represent numbers that you are trying to calculate.
- Read the question multiple times before and after forming your equation.
- Once you have formed your equation you can solve it.
- Remember to answer the question.
• Solve simple linear inequalities that involve reversing the inequality sign.
• Solve simple linear inequalities that involve reversing the inequality sign.
- If you multiply or divide by a negative sign you must FLIP the inequality.
- Remember 2<3 but -2>-3
- Otherwise inequalities require the same skill set as solving.
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