86 
THE APPLICATION' OP A LG EliR A 
PROBLEM XXIII. 
A gentleman hired a servant for ] 2 months, and agreed 
to allow him 20l. and a livery, if he staid till the year 
was expired; hnt at the end of 8 months the servant went 
away and received 12l. and the livery, as a proportional 
part of his wages: the question is, what was the livery 
valued at J 
Let x be the value sought; then 20 p .r will be the 
whole wages for 12 months, and 12 | x the part there 
of which he received for 8 months 
But the wages being in the same proportion as the 
times in which they are earned, or become due, we 
therefore have, as 12 : 8 :: 20 t- x : 12 P .r; whence 
12 X 12 P £' — 8 X 20 P x, or 1 1 1 P 12.T = 160 P SA' 
(by Theor. l. p. 72) consequently I2.r — 8.r — l(50 — 
. 1(5 , 
144, and x — -y- — 41, 
PROBLEM XXIV. 
Four persons A, B, C, D, spent twenty shillings in 
company together; whereof A proposed to pay -j; ; 
C-f; and pi part; hnt, when the money came to he col 
lected, they found it was not. sufficient to answer the in 
tended purpose: the question then is, to find how much 
each person must contribute, to make up the whole reck 
oning, supposing their several shares to he to (ach other 
in the proportion above specified ? 
Let a’ be the share of A; then it will bc^ as 
■y • b OT, as 4 : 3 ■: 
ii 
the share of B; 
and, as 
? : !, or, as 5 : 3 :: 
3 V 
the share of C ; 
also, as 
: i, or, as 2:1: 
X 
o 
the share of D. 
Therefore by the 
question, x 
3.r 3x 
' - 4 »--* ' 
Ö 
c* 
II 
H 1 “u 
v. hence, 40.1' -p 30.r V 24.r 1 
2Q.r — 800, that 
is 1 li.r