Then, by 1st condition, ar+y i qk«_

and by 2d condition, x+y ^

from which we have a;=85, and y=35 5

[ Page 107. ]

(7-)

Let x= the number of guineas, and y= the number of
moidores used

Now it is evident that the number of pieces used, of each



[ 107 ] 17

kind, multiplied by the number of shillings ih the piece, will
give the number of shillings paid in that particular kind of
money. That is, 21a; will be the number of shillings paid in
guineas, and 27y the number paid in moidores. Then ob-
serving that the whole bill JS120=:2400j., we have,
by 1st condition, a;+y=100,

by 2d condition, 21a;+27y=2400 ;

which give jc=50, and y=r50.
(8.)

Let x=i the distance travelled by the first, and y= the dis-
tance travelled by the second ;
Then ir+y=150.
But since the first travels 8 miles, while the second travels
but 7, the distance which they respectively travel will be in
the proportion of 8 to 7 : that is

a? : y : : 8 : 7 ;
or 7a;=8y;

from which we find a;=:80, and y=70 ; and if the entire
distance travelled by each be divided by the distance trav-
elled each day, the quotient will be the time, 10 days.
(9.)

Let x=z the number cast for the first, and y= the number
cast for the second.
Then a?-l-y=375,

and ar— y=91 ; •

which give aEr=:233, and y=142.
