CHAPTER IX.
Problems Leading to Simple Equations.
85. The principles of the last chapter may now be employed to solve various problems.
The method of procedure is as follows : Represent the unknown quantity by a symbol, as x, and express in symbolical language the conditions of the question ; we thus obtain a simple equation which can be solved by the methods already given in Chapter vii.
Note. Unknown quantities are usually represented by the last letters of the alphabet.
Ex. 1. Find two numbers whose sum is 28, and whose difference is 4.
Let x represent the smaller number, then x +4 represents the greater.
Their sum is x+ (x + 4), which is to be equal to 28. Hence x + x +4 = 28 ; 2 x= 24 ; x= 12, and x + 4 = 16,
so that the numbers are 12 and 16.
The beginner is advised to test his solution by proving that it satisfies the conditions of the question.
Ex. 2. Divide 60 into two parts, so that three times the greater may exceed 100 by as much as 8 times the less falls short of 200.
Let x represent the greater part, then 60 — x represents the less.
Three times the greater part is 3 x, and its excess over 100 is 3x-100.
Eight times the less is 8(60 — x), and its defect from 200 is 200 - 8(60 - x).
