### Algebraic Equations - word problems

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.

E.g.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.

E.g.2

I think of a number, take away 5 and the answer is 10. Find the number.
Let the number be x. x - 5 = 10
+ 5 => x -5 + 5 = 10 + 5
x = 15
The number is 15.

E.g.3

I think of a number, multiply by 3 and the answer is 30. Find the number.
Let the number be x.
3x = 30
:- 3 => 3x / 3= 30 /3
x = 10
The number is 10.

E.g.4

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.

E.g.5

I think of a number, divide by three, add 7. The answer is 10. Find the number.
Let the number be x. x/3 + 7 = 10
-7 => x/3 + 7 - 7 = 10 - 7
x/3 = 3
X 3 => x/3 X 3 = 3 X 3
x = 9
The number is 9.

E.g.6

I think of a number, take away three and then divide by 4. The answer is 3. Find the number.
Let the number be x.
(x - 3) / 4 = 3
X 4 => (x-3) /4 X 4 = 3 X 4
(x-3) = 12
+ 3 => x - 3 + 3 = 12 + 3
x = 15
The number is 15.

E.g.7

I think of a number, multiply by 3, add 3. The answer is the same, if I add 10 to the number. Find the number.
Let the number be x.
3x + 3 = x + 10
-3 => 3x + 3 -3 =x + 10 - 3
3x = x + 7
- x => 3x - x = x - x + 7
2x = 7
:-2 => 2x / 2 = 7 / 2
x = 3.5
The number is 3.5.

E.g.8

I think of a number, multiply by 2, take away 4. The answer is the same if I multiply it by 5 and then add 8. Find the number.
Let the number be x.
2x - 4 = 5x + 8
+4 => 2x - 4 + 4 = 5x + 8 + 4
2x = 5x + 12
-5x => 2x - 5x = 5x - 5x + 12
-3x = 12
:--3 => -3x/-3 = 12 / -3
x = -4
The number is -4.

E.g.9

The width of a rectangle is 2cm less than the length. The perimeter is 20 cm. Find the length and the area.
let the width be x. So, the length = x + 2.
x + x + 2 + x + x + 2 = 20
4x + 4 = 18
-4 => 4x + 4 - 4 = 20 - 4
4x = 16
:-4 => 4x / 4 = 16 / 4
x = 4
Width = 4cm; length = 6cm;
Area = 24 cm2.

E.g.10

The sum of two consecutive odd numbers is 52. Find the numbers.
Let the first number be x. Then the next one is x + 2.
x + x + 2 = 52
2x + 2 = 52
-2 => 2x + 2 - 2 = 52 - 2
2x = 50
:-2 => 2x / 2 = 50 / 2
x = 25
The numbers are 25 and 27.

This is the book on the new GCSE Mathematics 9-1 Topics: lots of worked examples for progressive training

Now, in order to complement what you have just learnt, work out the following questions:

1. I think of a number, multiply by 4 and add 5. The answer is 29. Find the number.
2. I think of a number, add 3 and the result is multiplied by 4. The answer is 28. Find the number.
3. I think of a number, add 6 and divide by 3. The answer is 5. Find the number.
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.
5. Twice a number added to 5 is the same as the number added to 10. Find the number.
6. A number multiplied by 5, add 4 is the same as 6 times the number. Find the number.
7. Three times a number, add nine, divided by 6 is the same as the number itself. Find the number.
8. Twice a number added to 6 is the same as ten subtracted from six times the number. Find the number.
9. The sum of three consecutive numbers is 78. Find the numbers.
10. The sum of three consecutive even numbers is 44. Find the numbers.

### Resources at Fingertips

This is a vast collection of tutorials, covering the syllabuses of GCSE, iGCSE, A-level and even at undergraduate level. They are organized according to these specific levels.
The major categories are for core mathematics, statistics, mechanics and trigonometry. Under each category, the tutorials are grouped according to the academic level.
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