78 
THE APPLICATION’ OF ALGEBRA 
Let the number sought be represented by 
then will its quadruple be denoted by .... 
x; 
4 A'; 
whence, by the conditions of the question, x 75 = 4.r; 
this equation, by transposing x, becomes .... 75 = 3x; 
75 
from whence, dividing by 3, we have x — ~ = l 25, 
which is the number that was to be found (for it is 
plain that 25 + 25 X 3 = 25 X 4 r 100). 
PROBLEM II. 
What number is that, which being added to A, and also 
multiplied by A,the product shall be the triple of the sum? 
Let the number sought be denoted by x; 
so shall the sum be denoted by 
and the product by 
whence, by the conditions of the question, 4.r = 
,t + 4 x 3; that is, Ax — 3x t- 12; from which by 
transposition, x = 12. 
PROBLEM III. 
To find two numbers such, that their sum shall be 30, 
and their difference 12. 
If x be taken to denote the lesser of the two numbers; 
then, by adding the difference 12, the greater number 
will be denoted by x f 12; and so we shall have 
2.r -f 12 = 30 by the question. 
From which equation, 2x = 30—12 = 18; and conse- 
1 8 
quently a’ = = 9; whence the greater number 
(a f 12) is also given = 21. 
PROBLEM IV." 
To divide the number GO into three such parts, that the 
frst may exceed the second by 8, and the third by 16. 
Let the first part be denoted by x; then the second 
will be'x— 8, and the third x—16; the aggregate of 
all which, or 3.r — 24 is = 60, by the question.