that is, the man will drink

of the beer in a single day;

and hence, the whole of it in 20 days.

(13.)

Let the fresh water to be added be denoted by x. Then, the amount of the mixture will be denoted by x + 32. But the addition of the fresh water will not increase the quantity of salt in the 32 lbs. of salt water; hence, the x + 32 pounds of the mixture will contain one pound, or 16 ounces, of salt. But, by the conditions of the question, 32 lbs. of this mixture are to contain 2 ounces of salt;

In this example, we must bear in mind that, if the rate of interest be divided by 100, and the quotient multiplied by the principal, the product will always be the amount of interest.

Let x denote the greater part, and y the lesser.

(15.)

Denote the number of votes received by the successful candidate, by x, and the number received by the other, by y. Then, by the first condition,

x y1500.

Had the first received of y in addition, the second would have received y tyy, and we should have,

Let x denote the value of the gold watch, and y that of the silver watch.

The separate figures which are placed by the side of eacl other, in order to express any number, are called digits. Now, from the relative value of these figures, resulting from the places which they occupy, we can easily see how the numbers may be expressed. For example, if the number is

expressed by two digits, then the first figure on the right, plus ten times the second figure, will always give the number. Thus,

36 = 3 × 10+ 6; and, 87 8 x 10 + 7, &c.

If the number is expressed by three figures, then one hundred times the left-hand figure, plus ten times the middle figure, plus the right-hand figure, will express the number. Thus,

246 100 x 2 + 10 × 4 + 6 = 200 +40 + 6 = 246. the left-hand digit, and y = the other.

Let

Then,

also,

from which we have,

x + y = 11;

x + 13 = 3y;

Let x denote the number of gentlemen, and y the num ber of ladies. Then, y 15 the ladies who remained,

=

the conditions of the question,

x = 2(y15) 2y - 30,

And, by

=

Let x denote the value of the horse in dollars, and y the number of tickets. If he sells the tickets at $2, he will receive $2y; if at $3, he will receive $3y.

(20.)

Let x denote the number of bushels of wheat purchased, and y the number of bushels of rye.

Let x denote the number A took, and y the number B

Let a denote the number of dollars which A has, and y the number B has.

Then, x + 3y = 1200, and y + x = 1200:

from which we find,

x = 800, and y = 600.

(23.)

Let x denote the price of the brandy, and y that of the sherry.

If, now, we make the first mixture, that is, two dozen of sherry and one dozen of brandy, the mixture itself will contain three dozens, and will, consequently, be worth 78s. × 3 = 234s. Hence, we have,

2x + y = 234, for the first, and,
7x+2y = 79 X 9 = 711, for the second;

Let x, y, and z denote the separate ages of A, B, and C.

x = 84, y = 42, and z = 14.

Or, this example may be solved with a single unknown

quantity. Thus: let C's age; then,

x =

and,

C's age = x,

B's age 3x,

A's age 6x,

x + 3x + 6x = 10x = 140;