Equations and inequalities · Ages 12–13
From words to an equation worksheet
Part of: Linear equations in one unknown
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From words to an equation worksheet
Equations and inequalities · Ages 12–13
Numsprite
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Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.3 bags, x sweets in each, 1 extra: 67 in all. The equation: x + = .
Fill in each blank
Answer:
2.3 bags, x sweets in each, 7 extra: 88 in all. The equation: x + = .
Fill in each blank
Answer:
3.Ka-lok has 4 times as much money as Tsz-hin. Ka-lok spends $45 and Tsz-hin is given $3, and then they have the same. With $x as Tsz-hin's at first: Ka-lok now has $(x − 45), Tsz-hin has $(x + ), and solving gives x = .
Fill in each blank
Answer:
Part B: Choose, or true or false (2 marks each)
4."4 less than 8 times x is 45": which equation is it?
- A. 8x − 4 = 45
- B. 8x + 4 = 45
- C. 4 − 8x = 45
- D. 8(x − 4) = 45
Choose the right answer
Answer:
5."10 added to 8 times x makes 44": which equation is it?
- A. 10x + 8 = 44
- B. x + 8 + 10 = 44
- C. 8(x + 10) = 44
- D. 8x + 10 = 44
Choose the right answer
Answer:
6."11 less than 4 times x is 14": which equation is it?
- A. 11 − 4x = 14
- B. 4(x − 11) = 14
- C. 4x + 11 = 14
- D. 4x − 11 = 14
Choose the right answer
Answer:
7.Dad is 60 and the child x now. In 9 years, Dad will be 3 times the child's age. Which equation is right?
- A. 60 + 9 = 3x
- B. 60 + 9 = 3(x + 9)
- C. 60 = 3(x + 9)
- D. 60 + 9 = 3x + 9
Choose the right answer
Answer:
8."4 times the number 9 less than x is 14" can be written 4x − 9 = 14.
True or false?
Answer:
9.May buys 2 pens at $y each, pays $19 and gets $3 change. Which equation is right?
- A. 19 − 2y = 3
- B. 2y − 19 = 3
- C. 2y + 19 = 3
- D. 19 − y = 3
Choose the right answer
Answer:
10.Three consecutive whole numbers add up to 174. With x as the middle one, which equation is right?
- A. x + 2x + 3x = 174
- B. (x − 1) + x + (x + 1) = 174
- C. x + (x + 1) + (x + 2) = 174
- D. (x − 1) + (x + 1) = 174
Choose the right answer
Answer:
11.Chi-keung has 2 more cards than May, 20 altogether. With x as Chi-keung's, which equation is right?
- A. x − (x − 2) = 20
- B. x + (x − 2) = 20
- C. x + (x + 2) = 20
- D. 2x = 20
Choose the right answer
Answer:
12.Tsz-ching has 11 more cards than Ka-lok, 57 altogether. With x as Tsz-ching's, which equation is right?
- A. x + (x + 11) = 57
- B. x − (x − 11) = 57
- C. x + (x − 11) = 57
- D. 2x = 57
Choose the right answer
Answer:
Part C: Word problems (4 marks each)
13.Dad is 35 and the child 14. In x years, Dad will be 2 times the child's age. Which equation is right?
- A. 2(35 + x) = 14 + x
- B. 35 + x = 2 × 14 + x
- C. 35 = 2(14 + x)
- D. 35 + x = 2(14 + x)
Choose the right answer
Working:
Answer:
14.Chi-keung eats 17 of a box of chocolates, then 3 more, leaving 27. With x at first, which equation is right?
- A. x − x7 − 3 = 27
- B. x − 17 − 3 = 27
- C. x − x7 + 3 = 27
- D. x7 − 3 = 27
Choose the right answer
Working:
Answer:
15.Two people 72 km apart walk towards each other at 6 km/h and 3 km/h, and meet after x hours. Which equation is right?
- A. 6x + 3 = 72
- B. 6 + 3 + x = 72
- C. 6x − 3x = 72
- D. 6x + 3x = 72
Choose the right answer
Working:
Answer:
16.May has 42 cards and Tsz-ching has 38. After May gives Tsz-ching x cards, they have the same. Which equation is right?
- A. 42 − x = 38 + x
- B. 42 + x = 38 − x
- C. 42 − x = 38
- D. 42 − x = 38 − x
Choose the right answer
Working:
Answer:
17.$5 and $2 coins, 15 in all, are worth $51. With x $5 coins, which equation is right?
- A. x + (15 − x) = 51
- B. 2x + 5(15 − x) = 51
- C. 5x + 2(15 − x) = 51
- D. 5x + 2x = 51
Choose the right answer
Working:
Answer:
18.x spiders (8 legs), other beetles (6): 12, 76 legs. x + (12 − x) = 76, x = .
Fill in each blank
Working:
Answer:
Show the answers and working
From words to an equation worksheet: Answers and working
Part A: Working out and filling in
1. 3, 1, 67
3 bags hold 3x, plus 1, make 67: 3x + 1 = 67.
2. 3, 7, 88
3 bags hold 3x, plus 7, make 88: 3x + 7 = 88.
3. 4, 3, 16
Ka-lok had 4x, and after spending 45 has 4x − 45; Tsz-hin with 3 more has x + 3. The same: 4x − 45 = x + 3, so x = 16.
Part B: Choose, or true or false
4. A. 8x − 4 = 45
8 times x is 8x, and 4 less than that is 8x − 4.
5. D. 8x + 10 = 44
First 8 times x is 8x, then add 10, making 44.
6. D. 4x − 11 = 14
4 times x is 4x, and 11 less than that is 4x − 11.
7. B. 60 + 9 = 3(x + 9)
In 9 years both gain 9: Dad 60 + 9, the child x + 9.
8. False
"9 less than x" is x − 9, and 4 times that is 4(x − 9) = 4x − 36.
9. A. 19 − 2y = 3
2 pens cost $2y. Pay $19, take the cost away, and $3 is the change.
10. B. (x − 1) + x + (x + 1) = 174
The middle is x, the one before x − 1, the one after x + 1; together 174: (x − 1) + x + (x + 1) = 174. Try x = 58: 174, right.
11. B. x + (x − 2) = 20
Chi-keung has x, and May has 2 fewer, x − 2. Together 20: x + (x − 2) = 20.
12. C. x + (x − 11) = 57
Tsz-ching has x, and Ka-lok has 11 fewer, x − 11. Together 57: x + (x − 11) = 57.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. D. 35 + x = 2(14 + x)
In x years: Dad 35 + x, the child 14 + x; and Dad is 2 times the child.
14. A. x − x7 − 3 = 27
x at first, x7 eaten, then 3 eaten, 27 left.
15. D. 6x + 3x = 72
When they meet, their two distances make the whole gap: 6x + 3x = 72.
16. A. 42 − x = 38 + x
May ends with 42 − x and Tsz-ching with 38 + x, and those match.
17. C. 5x + 2(15 − x) = 51
x $5 coins and 15 − x $2 coins; value = number × face value.
18. 8, 6, 2
x spiders have 8x legs; 10 beetles have 6(12 − x); this gives x = 2.
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