108 
THE APPLICATION OF ALGEBRA 
ceived 18 faj pence for them; hut, replies B, had I 
brought no more than you, I should hate received only 8 
(b) pence for mine: the question is, to find how many 
eggs each person had ? 
If the number of eggs which A had be = x, the 
number of B’s eggs will be — c — a?; therefore, by the 
ax 
— the num- 
problem, it will be, c— x : a :: x 
ber of pence which A received; and as x : b :: c — x ; 
h x c 
x 
— the number of pence which В received; 
ax b x c—x 
whence, again, by the problem, 
; and 
therefore ах ъ rz b x c — x* — be 2 — 2bex -f Jar 1 ; 
2bex be 2 
which equation, ordered, gives х г + 
a — b 
from whence x comes out ( 
= у/ 
be 2 
a — b 
a — ¿Г 
_ -^t) = cs//(lf) — 40. But the value of x may 
a—b a—b J 
be otherwise, more readily, derived from the equation 
ax z zz b x c — x Г, without the trouble of completing 
the square; for the square root being extracted on both 
sides thereof, we have x \/ a — c —x x \/ 6; whence 
x >ya f .r >yb ~ c >yb, and consequently x ~ ( — 
100v/8 100a/4 _ . . 
— — — 40 as before. 
v/18 + v/8 л/9 + л/4 * J 
PROBLEM LIV. 
One bought 120 pounds of pepper, and as many of gin 
ger, and had one pound of ginger more for a crown than of 
pepper; and the iclwle price of the pepper exceeded that 
of the ginger by six crowns: how many pounds of pepper 
had he for a crown, and how many of ginger/ 
Let the number of pounds of pepper which he had 
for a crown be x, and the number of pounds of ginger