186 
THE RESOLUTION OF 
cording to the preceding note, the question can have 
only one answer, in whole numbers. 
problem VI. 
A certain number of men and women being merry-ma- 
king together, the reckoning came to 33 shillings, towards 
the discharging of which, each man paid 3s. 6d. and each 
woman Is. 4d.: the question is, to find how many persons 
of both sexes the company consisted of ? 
Let x represent the number of men, and y that ot 
the women; so shall 42.r -f 16y = 396, or 2lr -f by 
jog 2 IT 
— 198; and consequently y — rr 24 — 2x 
8 
5t — 6 , , , , , 5x — 6 
—: whence, y being a whole number, 
must likewise be a whole number ; and the value of 
x, answering this condition, will be found — 6; and 
consequently that of y (= 24 — 12 — 3) — 9; which 
two will appear to be the only numbers that can an 
swer the conditions of the question; because 21, the co 
efficient of x, is here greater than 9, the greatest value 
of y. 
PROBLEM VII. 
One bought 12 loaves for 12 pence, whereof some were 
two-penny ones, others penny ones, and the rest farthing 
ones: what number were there of each sort ? 
Put x — the number of the first sort, y — that of 
the second, and z that of the third; and then, by 
the conditions of the question, we have these two equa 
tions, viz. 
x + y + z - 12, and 
8t -f- 4y -f z — 48. 
AVhereof the former being subtracted from the latter, 
in order to exterminate c, we thence get Jx f 3y — 36, 
and therefore y— - — 
3 
whence 
3 
it is evident that the value of r = 3. and consequently 
that ?/ = 5, and z — 4 ; which are the numbers that 
were to be found.