"MJ 
. 'rnr —«v 
82 
THE APPLICATION 01 ALULBRA 
by reduction, 12X 4 $v 1 Qx — 576 = 24r; therefore 
• 576 
2a: r: 576, and x — ~ — 288. So that there were 
128 lb. of copper, 84 lb. of tin, and 76 lb. of lead. 
PROBLEM XIV. 
What sum of money is that, from which 5l. being sub 
tracted, two thirds of the remainder shall be 401.? 
Let x represent the required sum; then, 5 being sub 
tracted, there will remain x— 5; two thirds of which 
will be x—5 x -j, or 
2r—to 
; and so, by the question, 
, 2 V — 10 ^ . 
we have =: 40 : whence 2 r— 10 ~ 120; 
and x — 
— 65. 
PROBLEM XV. 
What number is that, which being divided by 12, the 
quotient, dividend, and divisor, added all together, shall 
amount to 64? 
Let v = the required number; so shall 
-f- pc t- 12 — 64, by the conditions of the question. 
Whence x 4- 12V — 52 X 12, or I3v z= 624; and con- 
, 624 
sequently x — -y = 48. 
PROBLEM XVI. 
To find two numbers in the proportion of 2 to 1, so that, 
if 4 be added to each, the two sums thence arising shall 
be in proportion as 3 to 2. 
Let x denote the lesser number; thendhe greater will 
be denoted by 2a?; and so, by the question, we shall have 
ix + 4 : x 4- 4 :: 3 : 2. From whence, as the product 
of the two extremes, of any four proportional num 
bers, is equal to the product of the two means, few