ELEMENTARY ARITHMETIC.

PART III,

CHAPTER I.

BILLS OF PARCELS.

1. A person who receives money, goods, or services from another, is called a debtor; and a person who parts with money, goods, or renders services to another, is called a creditor.

2. A Bill is a written account of goods sold or delivered, or of services rendered, with the price or value attached to each item.

3. When the Bill refers to goods bought or sold at a single transaction, and containing only one date, it is called a Bill of Parcels.

4. But when it contains a statement of goods bought or sold at different dates, as copied from a tradesman's books, it is called a Bill of Book Debts.

5. The following abbreviations are generally used in bills, or accounts, as they are sometimes called:Dr. for debtor; Cr. for creditor; for account; @ for at, this abbreviation is always followed by the price of a single unit. Thus, 3 lbs. of sugar @ 64d., means 3 lbs. of sugar at 61d. per lb.

(1) A poulterer gains 1d. a score on eggs, id. a lb. on butter, and 9d. a couple on fowls; if he sell Io score of eggs and 43 lbs. of butter, how many fowls must he sell to gain 8s. altogether?

(12) A goldsmith manufactured 3 lbs. 8 dwts. of gold into rings, each containing 9 dwts. 8 grs. ; he sold the rings at £2 6s. 8d. each; how much did he receive for them?

MISCELLANEOUS EXAMPLES.

A father is five times as old as his son, and the difference of their ages is 28. Find the son's age.

Since the father is 5 times as old as the son, the difference of their ages is 4 times the son's age.

Therefore 4 times the son's age = 28 years;
And, therefore, the son's age

=

7 years.

A publican buys 9 barrels of beer at £1 19s. per barrel. Three of the casks being leaky, he loses thereby 27 gallons. At what rate per pint must he sell the remainder in order to gain £7 45. on his outlay?

Bought 9 barrels, or 324 gallons.
Lost by leakage

27

Cost of 9 barrels at 39s. per barrel = 3515.

Gain on the whole

Selling price of 297 gallons

= 144.

= 4955.

Therefore the selling price of 1 gal. = 4955. 297.

= IS. 8d.

= IS. 8d.÷8.

The cost of a second-class railway ticket is double that of a third-class ticket, and of a firstclass half as much again as that of a second class. Five first-class tickets, four second-class tickets, and nine third-class tickets, for a journey of 90 miles, amount to £12. Find the price of each ticket, and the rate per mile for the second class. Cost of a second-class ticket

cost of 2 third-class.

=

Therefore the cost of 5 first, 4 second, and 9 third class tickets is the same as the cost of 32 third class. Therefore the cost of 32 third class = £12.

1. Express in words 203,008,065; in figures, eighty million seventeen thousand and six; and in Roman numerals, 789.

2. Add together 87,397, five hundred and eightynine, four thousand six hundred and seventy-eight, 38,094, MDCCCLXXV. and CCCXCVII.

3. Find the difference between three million four thousand and sixty-five and twenty-nine thousand eight hundred and seventy-three.

4. Multiply 3,867,495 by 4,786; and 73,896,250 by 640,800.

. 5. Divide 4,354,554 by 59; and 2,361,671 by the factors of 63, and find the remainder.

6. Reduce £497 18s. 5d. to farthings; 318,759 halfpence to pounds; and five thousand three hundred and eighty-seven guineas to half-crowns.

7. Add together £87 135. 93d., £594 18s. 10td., £68 15s. 4d., three hundred and ninety-seven pounds nineteen shillings and sevenpence three farthings, £86 7s. 8d., nine pounds fifteen shillings, and £4.738 14s. 11d.

8. Find the difference between ten thousand and eighty-seven pounds ten shillings and fourpence, and nine hundred and ninety-seven pounds nineteen shillings and sevenpence halfpenny.

9. Multiply £39 17s. 93d. by 49; forty-seven pounds sixteen shillings and fivepence farthing by eighty-seven; and fifty-seven pounds nine shillings and tenpence three farthings by four hundred and sixty-three.

10. Divide £3,174 15s. 7 d. by the factors of seventy-two; £2,189 125. 1old. by 473; and twenty-nine pounds fourteen shillings and eightpence halfpenny by thirteen shillings and nine

pence.

11. What will be the wages of twenty-one persons for seventeen days, if each earn two shillings and sevenpence halfpenny a day?

12. A man bought two farms, one containing eighty-nine acres at four pounds an acre, and the other containing two hundred and seventy-nine acres at three pounds ten shillings an acre. was the whole cost?

What