(20.)

Let the sum at interest be denoted by x.

Then, since the interest which accrues on any sum for a year, is equal to the sum multiplied by the rate, divided by 100, we shall have,

or,

100 = 2940;

400x125x = 36750000; or, x = 70000.

(21.)

There are several ways in which this example may be solved :

First. We see by the conditions, that the first cock will discharge one gallon in a minute, the second cock half a gallon in a minute, and the third cock one-third of a gallon in a minute. Hence, the quantity discharged by the three cocks in a minute, is equal to

gals. 60 gals. :: 1 m. : 32 minutes.

But, to resolve the question in a general way, without regard to the contents of the cask, let z denote the part of

the cask which would be emptied in a single minute. Then, as the first cock would empty of the cask, the second To of it, and the third of it, in one minute, we have,

Now, as

of the cask is emptied in one minute, it is evident that to empty the entire cask will require as many minutes as the number 1 contains ; that is, 32

(22.)

Let the number of trees in the orchard be denoted by a

Let the number of sheep be denoted by . Then, by observing the statement of the last problem, we have,

Let x denote the amount of rent last year.

Then,

8x 100

equal the excess of the present over the past

year, and the rent of the present year will be expressed by

Let the number of beggars be denoted by x. Then, by the conditions,

also,

3x 8 = the amount of money he had;

2x + 3 = the amount of money

Hence, 3x

8 = 2x + 3, or x = 11.

(30.)

Let x = the number of shillings which he had.

= what he first lost;

1

+ 3 = what he had left after borrowing

Then,

2x + 3
3

=

3x + 12
12

= what he lost the second time;

and this, taken from +3, or what he had at the commencement of the second game, will give what he had left;

(31.)

Let x denote the amount laid out by each.

Then,

x + 126 = what A had, after gaining,

what B had, after losing.

and,

87

Let x denote the sum which he had at first. Then, x 2 = what he had after spending;

2x

and, 2x

4x

and, 4x

then,

Hence,

what he had after borrowing,

what he had after spending at second

tavern ;

what he had after borrowing,

what he had after spending at third

tavern ;

8x28, what he had after borrowing, and

8x 30s. = 0.

x = 38. = 3s. 9d.

(33.)

denote the number of yards in the piece.

3x 57

Let

Then,

and,

what remained of the first 3 pieces, what remained of the fourth piece.

142 yards, what remained in all.

4x = 142 + 74; or, x = 54.