Algebraic Equations – Word Problems

Asad Aziz

An equation is almost a sort of seesaw: you add something to the left, lose the balance and are forced to do the same to the right; you divide and multiply by something, once again, the same must be done to the other side; if you subtract something, there is no exception. Therefore, solving equation means, getting rid of everything around x by seesaw method.

Example 1

I think of a number, add 7 and the answer is 10. Find the number.

Let the number be x.

x + 7 = 10

-7 => x + 7 -7 = 10 -7

x = 3

The number is 3.

Example 2

I think of a number, multiply it by 2, take away 4. The answer is 10. Find the number.

Let the number be x. 2x – 4 = 10

+ 4 => 2x – 4 + 4 = 10 + 4

2x = 14

:- 2 => 2x / 2 = 14 / 2

x = 7

The number is 7.

Practice Questions

1. I think of a number, multiply it by 4 and add 5. The answer is 29. Find the number.

Ans: 6

2. I think of a number, add 3 and the result is multiplied by 4. The answer is 28. Find the number.

Ans: 4

3. I think of a number, add 6 and divide by 3. The answer is 5. Find the number.

Ans: 9

4. I think of a number, multiply by 4, and add 6. The result is then multiplied by 5 and the answer is 70. Find the number.

Ans: 2

5. Twice a number added to 5 is the same as the number added to 10. Find the number.

Ans: 5

6. A number multiplied by 5, add 4 is the same as 6 times the number. Find the number.

Ans: 4

7. Three times a number, add nine, divided by 6 is the same as the number itself. Find the number.

Ans: 3

8. Twice a number added to 6 is the same as ten subtracted from six times the number. Find the number.

Ans: 4

9. The sum of three consecutive numbers is 78. Find the numbers.

Ans: 25, 26, 27

10. The sum of three consecutive even numbers is 60. Find the numbers.

Ans: 18, 20, 22

11. The sum of the half, the third and the forth of a number is 10 more than the original number. Find the number.

Ans: 120

12. The sixth of a number exceeds the eight of the same number by 4. Find the number.

Ans: 96

13. Divide £110 among Amy, Basil and Clare in such a way that Amy has £10 more than Basil and Basil has £20 more than Clare.

Ans: 50, 40, 20

14. Find a number so that its half exceeds the sum of the fifth and the sixth of the same by 16.

Ans: 120

15. A man is twice old as his son is now. Eighteen years ago, he was 5 times as old as his son was then. How old is his son now?

Ans: 24

16. The length of a plank of wood is 2cm more than its width. If the length and width were 1cm and 3cm more, the plank would have been a square. Find the length and width of the plank.

Ans: 6, 4

17. Anil and Bisma shared £80 between them. When Bisma gives Anil £20, Anil has £12 more than Bisma. How much did they have at the beginning?

Ans: 26, 54

18. The sum of two numbers is 112. Find the numbers, if the difference between them is 48.

Ans: 80, 32

19. Find two numbers with a difference and a mean, 8 each.

Ans: 12, 4

20. The longest side of an isosceles triangle is 4cm more than the twice of each other side. Find the length of the longest side, if the perimeter is 44cm.

Ans: 24