Now, if we denote the number of slain by s,

from which three equations we find, x = 90, y = 55, and

2 = 670.

(15.)

Let x, y, and z, denote the sums which they respectively had at first.

what C had, after his division with A and B.

But these three last sums are all equal to each other, and

the sum of x, y, and z, is equal to 96. Hence, after reducing, we have,

from which we find, x = $52, y = $28, and z = $16.

(16.)

Let the parts be denoted by x, y, and z.

Instead of denoting the parts of the work done by A, B, and C, by x, y, and z, as in Example 6, page 156, let us denote the times in which each would perform the work, respectively, by x, y, and z, and denote the work to be done, by 1. Now, if it takes A, x days to do the work, he will, in one day, do a part of the work denoted by; hence,

1

= what B could do in a day,

y

I

=what C could do in a day;

and these, multiplied by any number of days, would give what each could do in those days. Hence,

Subtracting the second equation from the first, we have,

Then, adding the third to this, we have,

1

=

30

y = 30, and z = 60.

Now, the three together could do in one day,

of the work; hence, they could do the whole work in ten

Let x denote the greater number; then will denote

11

the less.

Denote the age of the elder by x; then

Let the two numbers be denoted by x and y.

Then, by first condition,

x2 + y2 = 117;

by second condition,

22 y2 = 45;

from which we have,

will denote

x = 9, and y = 6.

(6.)

Let the two numbers be denoted by x and y.

Then,

and,

hence,

y =