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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

 

 

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