Application of Simple Equation
Illustration 1
Five times of a number is 3 more than the two times of a number
Solution

Let the unknown number is x
then five times of number is 5x
and two times of number is 2x
and the sum of 2x and 3 is 5x
5x = 2x + 3
For solving this equation we transpose +2x from RHS to LHS
5x – 2x = 3       3x = 3            x = 1

Illustration 2
Construct an equation from the following sentences
(i)     The sum of 5 and a number is 11
(ii)     If 7 is subtracted from a number then we get 2
(iii)    The sum of three times of a number and 5 is equal to 8
(iv)     One fifth of a number is equal to 2

Solution
(i)     Let us say the numbers is x
Sum of 5 and a number = 5 + x
So the equation is 5 + x = 11
(ii)   Let the number is y
by subtracting 7 from the number we get
y –7
so the equation is y–7 = 2
(iii)   Let number is z
three times = 3z
Sum of 5 and 3z is 3z + 5
So the equation is 3z + 5 = 8
(iv)  Let the number is x
One fifth of number is x/5
So the equation is x/5 = 2

Illustration 3
Solve: 3x –2 = 1 and check the result.
Solution
By transposing (–2) to RHS
3x –2 + 2 = 1 + 2        3x = 3
Divide both side by 3 Check putting value of x = 1 in the LHS of the equation
LHS = 3 × 1 –2 = 3 –2 = 1 = RHS
LHS = RHS

Illustration 4
A’s age is 3 yrs less than two times A’s friend’s age. If A’ age is 5 yrs. Set up an equation to find A’ friend’s age.
Solution

Let the A’s friend age is x yrs.
Two times of x is 2x.
Age of A is 3 yrs less than 2x
So the equation is  2x –3 = 5
Where x is the A’s friend age.

Illustration 5
One number is 3 less than the two times of the other. If their sum is increased by 7, the     result is 37. Find the numbers.
Solution

Let one number = x
other number = 2x – 3
(x + 2x – 3) + 7 = 37       3x + 4 = 37             3x = 37 – 4                 3x = 33             x = 11
2x – 3 = 2 ´ 11 – 3 = 22 – 3 = 19
The two numbers are 11 and 19.

Illustration 6
Construct 2 equations starting with x = 1
Solution

(i)     Multiply both sides by 2
2x = 2
Subtract both sides by 1
2x – 1 = 1 