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60 Rh CHAPTER VIII.

Symbolical Expression.

82. In solving algebraic problems the chief difficulty of the beginner is to express the conditions of the question by means of symbols. A question proposed in algebraic symbols will frequently be found puzzling, when a similar arithmetical question would present no difficulty. Thus, the answer to the question "find a number greater than x by a " may not be self-evident to the beginner, who would of course readily answer an analogous arithmetical question, "find a number greater than 50 by G." The process of addition which gives the answer in the second case supplies the necessary hint; and, just as the number which is greater than 50 by 6 is 50 + 6, so the number which is greater than x by a is x + a.

83. The following examples will perhaps be the best introduction to the subject of this chapter. After the first we leave to the student the choice of arithmetical instances, should he find them necessary.

Ex. 1. By how much does x exceed 17 ?

Take a numerical instance ; " by how much does 27 exceed 17 ? " The answer obviously is 10, which is equal to 27 — 17. Hence the excess of x over 17 is x— 17. Similarly the defect of x from 17 is 17 — x.

Ex. 2. If X is one part of 45 the other part is 45 — x.

Ex. 3. How far can a man walk in a hours at the rate of 4 miles an hour ?

In 1 hour he walks 4 miles. In a hours he walks a times as far, that is, 4 a miles.