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Introduction

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

Find four consecutive odd numbers whose sum is 120.

(a)    Let the first odd number be x.

(c)    This means that the next odd number is x + 2, and the next is x + 4 and the next is x + 6.

Their sum is 120.

The equation is:

x + x + 2 + x + 4 + x + 6  = 120

(d)    Solve to get:

4x + 12 = 120

4x = 120 - 12 = 108

x = 108 ÷ 4 = 27

(e)    The numbers are x, x + 2, x + 4 and x + 6.

Using x = 27, we get the odd numbers 27, 29, 31 and 33.

(f)    27 + 29 + 31 + 33 = 120 so it works.