TO THE RESOLUTION OF PROBLEMS. 
S3 
ro. 
f -**- + — + - 20 - = 12 A 20 + 30 = 62, 
¡2 3 4 
_ i 24 60 1 °0 
For -p = 8 4- 15 + 24 = 4/, 
o 4 3 
— + = 6 + 12 + 20 - 38* 
4 5b 
!S0 
Be 
PROBLEM XXXIII. 
A gentleman left a sum o f money to be divided among 
four servants, so that the share of the first ivas \ the sum 
of the shares of the other three; the share of the second •§- 
of the sum of the other three; and the share of the third ^ 
of the sum of the other three; and it was also found that 
the share of the first exceeded that of the last by 14/.; the 
question is, what was the whole sum, and what was the 
share of each person 9 
Let the shares be represented by x, y, z, and u, re 
spectively, and let a — 14; then, by the question, we 
shall have 
y A- z -f u 
x — 
x -f z 4- u 
y = 3— * 
x + y A u 
■v — 
4 
u — x — a. 
Which equations, cleared of fractions, become 
2x — y A z A u, 
3y — x A z A u, 
4z — x A y A u t 
u — x — a. 
Now, if x be added to the first, y to the second, and 
z to the third, we shall get (a? A y A z A u) — 3x — 4y 
3x 3x 
— 5z; and from thence 2 r; —, and y — —f-; which 
5 4 
values being substituted in the first equation, we have 
3a: 13a- 
h u. or u — 
5 20 
3x 
2r — A 
4 
; but, by the 4th