... the number of guns = 90;

the number of seamen = 30 × 22 + 10 = 670,

and the number of soldiers

7×30 + 10

4

55.

92. A Shepherd, in time of war, was plundered by a party of soldiers, who took of his flock, and 1 of a sheep; another party took from him of what he had left, and of a sheep; then a third party took of what now remained, and of a sheep. After which he had but 25 sheep left. How many had he at first?

Let x = the number he had at first;

Now the second party took away of these + of a sheep; ... there remained

(3)-=--=-=-1;

4

6

32-3

6

2

then the third party took away half of these + of a sheep;

93. A man being at play lost of his money, and then won 3 shillings; after which he lost of what he then had, and won 2 shillings; lastly he lost of what he then had; this done he had but 12 shillings left. What had he at first?

Let 4x = the number of shillings required;

then after the first loss he had 3x, and afterwards 3x + 3;

2

after the second loss he had (3x + 3 3) = 2x + 2, and

afterwards 2x + 4.

3

Having lost of this, he had . (2x + 4) =

12x + 24 7

4. A Trader maintained himself for 3 years at the expence of £50 a year; and in each of those years augmented that part of his stock which was not so expended by thereof. At the end of the third year his original stock was doubled. What was that stock?

Let x = the number of pounds required;

then - 50 = the sum not expended; and with this he

traded;

and.(

50) = the sum he had at the end of the first

95. A Merchant buys a cask of brandy for £48, and sells a quantity exceeding three-fourths of the whole by 2 gallons at a profit of £25 per cent. He afterwards sells the remainder at such a price as to clear £60 per cent. by the whole transaction; and, had he sold the whole quantity at the latter price, he would have gained £175 per cent. Required the number of gallons contained in the cask.

12

Let 4x = the number of gallons;

then = the original price per gallon (in pounds),

12

: the first price of sale
: the latter price of sale

=

and the number required = 4x = 120 gallons.

36 ; X

96. Water flows uniformly into a cistern, capable of containing 720 gallons, through a pipe; and at the same time is discharged by a pump, worked by three men, who take four strokes in a minute; but this not being sufficient, the cistern becomes full in 6 hours; they therefore now put in another pump, of such power that the quantity discharged at one stroke by this pump is to the quantity discharged at one stroke by the former :: 2:3; but being obliged to detach one of their number to work the pump, the former pump makes only 10 strokes in 3 minutes, and the latter 5 strokes in two minutes; by which means the cistern is emptied in 12 hours. How much water was discharged by each pump at one stroke? and how much flowed in through the pipe in one minute?.

Let 3x = the number of gallons discharged by the first pump at one stroke;

.. 2x = the number discharged by the second,

and 12x = the quantity discharged by the first in one minute, when 3 men worked;

* 6 × 60 × 12x = the quantity discharged in six hours;
.. 6 × 60 × 12x + 720 = 720. (6x + 1) = the quantity in-

troduced through the pipe in that time.

Now when the additional pump is worked,

10x = quantity discharged by the first in one minute; and 5x = the quantity discharged by the second in one minute; .. 15 × 12 × 60 = the whole quantity discharged in 12 hours;

.. 158 × 720 = 720 × 2. (6x + 1) + 720;

or 150 = 12x + 3;

by transposition, 3x = 3,
and x = 1;

... the first discharged 3 gallons, and the second 2, at one stroke; and the quantity introduced by the pipe in one

minute

720 × (6x + 1)

= 2 × 7 = 14 gallons.

6 × 60

97. A poor man with a wife and seven children, found during a scarcity that he could only earn sufficient to procure of a white loaf of bread per day for each of his family, himself included. He therefore applied to the parishofficers for assistance, by whom being allowed a daily sum = his earnings, and mixed bread being made by order of Parliament, which was cheaper than white in the proportion of 4 to 5, he was now enabled to procure of a mixed loaf per day for each of the family (himself still included) and had 18. 71⁄2d. over. Required the sum allowed him by the parish.

Let x = the price of a white loaf (in pence);

and = what the parish allowed him;