will be sufficient to cover a floor that is 15 feet broad and

This and many other questions of a similar kind can more readily be worked by calculating the areas.

Thus if x be the required number of yards,

yds.

yds.

Then x 31.11. dividing by 9 to bring the feet into square yards.

37 1

x = 3.2.3. = 6313 yards.

Ex. 10. What length must be cut off a board 7 inches wide, to make a square foot?

Here x. 7: 12. 12 :: 1 : 1 .. x = 144 = 204 ins. or at once, since the area must be 144 ins.,

x.7 = 144 .. x =

144

=

204 inches.

Ex. 11. Bought 4 pockets of hops, each weighing 1 cwt. 1 qr. 21 lbs. at £4 2s. 6d. per cwt.

What is the cost?

F

: 4.

£ = £= £23 4s. 41d.

32

Ex. 12. What principal will gain £262 10s. Od. in 7 years at 5 per cent.?

£ £

F

F

Ex. 13. How much wine at £28 10s. per pipe must be given for 47 cwt. 2 qrs. of tobacco at 36s. per cwt.

Ex. 14. Bought goods at 17s. 6d. and sold them for 18s. 3d. What is the gain per cent.?

Ex. 15. Required the interest of £632 5s. 6d. for 72

Ex. 16. The hour and minute hand are together at 12 o'clock, when will they next coincide? The velocity of the minute hand is 12 times as great as that of the hour hand. Let the time be a minutes after one o'clock ?

Then x 60+ x :: 1 : 12.
12x60+x.; x = ኢዩ

= 5 min. after 1.

Ex. 17. A can do a piece of work in 12 days, and B in 14 days, in what time will they both together do the same 'work?

A's daily work is th; B's is th. Let x = the number of days,

then (+) x = 1

Ex. 18. What is the present worth of £700 due 9 months hence, allowing a discount of £5 per cent?

The present value of £105 due twelve months hence, at 5 per cent, is £100.

.. the present value of £103 due 9 months hence is £100.

£

..≈ 100 :: 700: 1033.

70000

4

56000

Ex. 19. A hare pursued by a dog had a start of 86 yards, but for every 5 yards the hare runs, the dog runs 7, how far will they run before the dog overtakes the hare? It is evident that the dog gains 2 yards for every 7 yards he runs, and therefore 43.7 = 301 yards is the result required. yds. yds. yds. yds. Or 7 x 2 : 86

.. x = 43.7 = 301 yards.

Ex. 20. How much tobacco at 36s. per cwt. must be given in barter for 3 pipes of wine at £28 10s. Od. per pipe? £ cwt. £ pipes,

By the Examples given what are termed the Rule of Three, the Rule of Three Inverse, and the Double Rule of Three, are reduced to a simple proportion. - Simple Interest, Discount, Commission, Insurance, Purchase of Stocks, and Partnerships are included under the same method. The old method of treating single and double position seems undesirable, if we allow that every youth ought to acquire a knowledge of the elements of Algebra. It is requisite to add a few definitions, but the rules for working questions will be most fitly learned by teaching the pupil how to think and deduce his own rules. Rules about Tare and Tret, or allowances made on the weights of goods, are very useless, for a pupil who has learned to think must at once perceive that he must deduct the allowance from the given weight before he calculates the price of a package.

INTEREST, is the sum of money allowed for the use of another sum : thus if A lends B 100£ any number of years at 5 per cent., A must receive 5£ for each year, and the whole sum back at the end of the period.

DISCOUNT, is the present value of a sum due at a future period: thus 100£ is the present value of 105£ due 12 months hence at 5 per cent.

COMMISSION, is the money paid to a factor, broker, or banker for his management of money affairs: thus stockbrokers charge or or £ per cent., for the transferring, selling or purchasing of stock.

INSURANCE, is the rate per cent. paid to individuals or companies, who undertake to pay the value of any property if it be lost, destroyed, or burned within a certain specified time, and the rate varies from £ to 5£ per cent., more or less.

PARTNERSHIPS or FELLOWSHIP, is the method of calculating what share of profit or loss individuals must pay or receive who have ventured certain sums of money for various periods in any speculation or venture.

Thus A, B, and C, subscribe respectively £750, £1250, and £1500, and gain by the venture £1000; what is each man's share?

Suppose, however, that A had risked his £750 for three months, and then B had joined him with £1250, and at the end of another three months C had joined him with £1500, and the whole time from the first had been twelve months then the time and money must be combined.

And 750. 12+1250.9+1500 .6=9000+11250+9000 =29250

And 29250 9000 1000

;

A's share.

=

307

.. The whole profit +3071 + 384, = £1000 EXCHANGE, is to find how much of the money of one country is equivalent to a given sum of another country.

By the Par of Exchange is meant the intrinsic value of the money of one country compared with that of another, according to the fineness of the coins.

The Course of Exchange is the sum of money of one country which is given for a fixed sum of another country. This is seldom at par, but varying according to the circumstances of trade. The calculations are evidently examples of proportion.

The arbitration or Comparison of Exchanges is the determining what the rate of exchange, called the par of arbitration, will be by paying at any place through intermediate places : thus, the exchange between England and America is 80 per cent., and between England and Amsterdam at 36s. 4d. Flemish for one pound British; what then is the arbitrated course of exchange between America and Amsterdam?