Simple equations worksheet

Part A: Working out and filling in

1. 1. x ÷ 7 = 9, x = 63

   x ÷ 7 = 9: undo it in reverse, 9 × 7 = 63, so x = 63

2. 2. 4x + 7 = 87, x = 20

   4x + 7 = 87: undo it in reverse, 87 − 7 = 80, 80 ÷ 4 = 20, so x = 20

3. 3. 3x = 21, x = 7

   3x = 21: undo it in reverse, 21 ÷ 3 = 7, so x = 7

4. 4. 3x + 23 = 77, x = 18

   3x + 23 = 77: undo it in reverse, 77 − 23 = 54, 54 ÷ 3 = 18, so x = 18

5. 5. 5x = 35, x = 7

   5x = 35: undo it in reverse, 35 ÷ 5 = 7, so x = 7

6. 6. 7x − 28 = 42, x = 10

   7x − 28 = 42: undo it in reverse, 42 + 28 = 70, 70 ÷ 7 = 10, so x = 10

7. 7. 7x + 9 = 93, x = 12

   7x + 9 = 93: undo it in reverse, 93 − 9 = 84, 84 ÷ 7 = 12, so x = 12

8. 8. 5x = 40, x = 8

   5x = 40: undo it in reverse, 40 ÷ 5 = 8, so x = 8

9. 9. x − 7 = 27, x = 34

   x − 7 = 27: undo it in reverse, 27 + 7 = 34, so x = 34

10. 10. x ÷ 2 = 12, x = 24

    x ÷ 2 = 12: undo it in reverse, 12 × 2 = 24, so x = 24

11. 11. x − 14 = 24, x = 38

    x − 14 = 24: undo it in reverse, 24 + 14 = 38, so x = 38

12. 12. x ÷ 3 = 9, x = 27

    x ÷ 3 = 9: undo it in reverse, 9 × 3 = 27, so x = 27

Part B: Word problems

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

1. 13. Tsz-hin buys 4 identical notebooks and a pen for $17, paying $69 altogether. How many dollars does each notebook cost? (Answer: 13 dollars)

   Let each notebook cost $y: 4y + 17 = 69, so y = 13

2. 14. A number is multiplied by 2, and then 13 is added. The result is 27. What is the number? (Answer: 7)

   Let the number be y: 2y + 13 = 27, so 2y = 27 − 13 and y = 7

3. 15. A number is multiplied by 9, and then 26 is added. The result is 53. What is the number? (Answer: 3)

   Let the number be y: 9y + 26 = 53, so 9y = 53 − 26 and y = 3

4. 16. Ka-lok buys 3 identical notebooks and a pen for $30, paying $69 altogether. How many dollars does each notebook cost? (Answer: 13 dollars)

   Let each notebook cost $y: 3y + 30 = 69, so y = 13

5. 17. Tsz-hin has 27 pencils, which is 9 fewer than 2 times as many as Ka-yee has. How many pencils does Ka-yee have? (Answer: 18 pencils)

   Let Ka-yee have y: 2y − 9 = 27, so y = 18

6. 18. Ka-yee has 23 stickers, which is 5 fewer than 2 times as many as May has. How many stickers does May have? (Answer: 14 stickers)

   Let May have y: 2y − 5 = 23, so y = 14