Algebra: Substituting Numbers with Formulae

The main purpose of algebra is to solve problems.

But first, we must "translate" the problems into algebra.

The procedure for translation is generally as follows:

(a)   Let a letter stand for the quantity to be found in the question.  (e.g.  Let the missing number be x)

(b)   State the units of measurement if necessary.  (e.g.  Let the distance be x metres)

(c)   Write statements involving the missing quantity and form an equation to connect them.

(d)   Solve the equation algebraically.

(e)   Translate the answer back into English.   (e.g.  the distance is 2.5 km)

(f)    Check the numerical answer with the facts given in the original question.

Example

I think of a number and multiply it by 6.  After adding 20 to the result, my answer is 2.  What is the number I first thought of?

(a)    Let the number I first thought of be x.

(c)    When I multiply by 6 and add 20, this becomes 6x + 20.  This is equal to 2.

        The equation is:

        6x + 20 = 2

(d)    Solve to get:

         6x = -18

         x = -3

(e)    The number I first thought of is -3

(f)    -3 × 6 = -18

       -18 + 20 = 2 so it works.