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Algebra Word Problems

 

Translate into equations and solve for the unknown.  

1. The sum of a number and twelve is twenty-one.

2. Five plus twice a number equals seventeen.

3. Half a number less five is nine.

4. The product of three and a number is twice their sum.

5. Four times a number plus eleven equals negative one.

6. Eight times a number less five times that number is twenty-four.

7. Twice a number divided into fifteen makes six.

8. Nine times a number minus three equals thirty-six.

9. Twenty increased by twice a number is fifty-two.

10. 7 less three times a number is -5.

11. The sum of a number and sixteen equals five times that number.

12. The sum of two consecutive numbers is fifty-five.

13. The sum of four consecutive numbers is fifty.

14. Two-thirds of a number less one-quarter of that number is 5.

15. Six more than one-sixth of a number is eighteen.

16. Three more than twice a number is thirty-one.

17. Two-thirds the sum of a number and nine is twelve.

18. Given three consecutive numbers, the sum of the second and third consecutive numbers is three times the first.

19. The sum of seven and twice a number is nineteen more than the number.

20. A rectangular garden plot is 8 m longer than it is wide. Find the dimensions and the area of the garden plot if it has a perimeter of 36 m.

21. A rectangular piece of plywood is 4 ½ times longer than it is wide. What is the length of the plywood if it has a perimeter of 2.2 m?

22. The sum of two numbers is 248. If one exceeds the other by 58, what are the two numbers?

23. A 12 m rope is cut into two pieces. If the longer piece is 1.5 m longer than the shorter one, find the length of the shorter piece of rope.

24. The perimeter of a rectangular room is 21 m. If the length is 1.5 m longer than the width, find the dimensions of the room.

25. A rectangular lot has a perimeter of 50 m. If the length is 5 m less than twice the width, find the dimensions of the lot.

 

Answers

 

1. 9

2. 6

3. 28

4. 6

5. -3

6. 8

7. 5/4

8. 7

9. 16

10. 4

11. 4

12. 27, 28

13. 11, 12, 13, 14

14. 12

15. 72

16. 14

17. 9

18. 3, 4, 5

19. 12

20. 5 m by 13 m, 65 m2

21. length = 0.9 m

22. 95, 153

23. 5.25 m

24. 4.5 m, 6 m

25. 10 m, 15 m

 

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