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, mutiply 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, mutiply 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 cm
2.
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.
Practice is the key to mastering maths; please visit this page, for more worksheets.
Now, in order to complement what you have just learnt, work out the following questions:
- I think of a number, multiply by 4 and add 5. The answer is 29. Find the
number.
- I think of a number, add 3 and the result is multiplied
by 4. The answer is 28. Find the number.
- I think of a number, add 6 and divide by 3. The answer is 5. Find the
number.
- 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.
- Twice a number added to 5 is the same as the number added to 10. Find the
number.
- A number multiplied by 5, add 4 is the same as 6 times the number. Find the
number.
- Three times a number, add nine, divided by 6 is the same as the number itself. Find
the number.
- Twice a number added to 6 is the same as ten subtracted from six times the number.
Find the number.
- The sum of three consecutive numbers is 78. Find the numbers.
- The sum of three consecutive even numbers is 44. Find the numbers.