equation, u xz x — a\ therefore x -— a zz ~—, and 
a? rr 
20a 
3 T 3r 
40: consequently y (-^-) — 30, 2 (, ) 
— 24, and a, (x — 14) — 2C; and the whole sum 
{x f y + : + n) zr 120/. 
PROBLEM XXXIV. 
To find four numbers, so that the first together with 
half the second may be 357 (a), the second 'with -j of the 
third equal to 476 (bJ, the third with ^ of the fourth 
equal to 5Q5 (cj, and the fourth with ~ of the first 
equal to 714 (dj. 
The required numbers being denoted by x, y, ~, and 
n, and the conditions of the question expressed in alge 
braic terms, we have the four following equations: 
F rom the first whereof we get x — a — ; and 
from the 4th, x — 5d — 5u; whence a — — 5d 5u, 
and y — 2a — lod F 10u; but, by the second, y = b — 
— therefore 2a — lod + \ou — b — ~ t and z — 3b 
3