(26) If 20 cwt. of tobacco cost £27..5..44; at what rate did Ans. £1..7..38.

I buy it per cwt.?

16

(27) What is the value of one hogshead of beer, when 120 hogsheads are sold for £154..17..10? Ans. £1..5..91. (28) Bought 72 yards of cloth for £85..6. What was the price per yard? Ans. £1..3..8 1. (29) Gave £275..3..4. for 18 bales of cloth. What is the Ans. £15..5..83 10. price of one bale? (30) A prize of £7257..3..6. is to be equally divided among 500 sailors. What is each man's share? Ans. £14..10..34388.

(31) A club of 25 persons joined to purchase a lottery ticket of £10. value, which was drawn a prize of £4000. What was each man's contribution, and his share of the prizemoney? Ans. each contribution 8s. and share of prize £160. (32) A tradesman cleared £2805. in 74 years; what was his yearly profit? Ans. £374. (33) What was the weekly salary of a clerk who received £266.18..1. for 90 weeks?

Ans. £2..19.3.

(34) If 100000 quills cost me £187..17..1. what is the price per Ans. £1..17..6 1.

thousand?

WEIGHTS AND MEASURES.

40

(35) Divide 83 lb. 5 oz. 10 dwts. 17 gr. by 8, 10, and 12. (36) Divide 29 tons, 17 cwt. O qrs. 18 lb. by 9, 15, and 19. (37) Divide 114 yards, 3 qrs. 2 nails, by 10, and 16. (38) Divide 1017 miles, 6 fur. 38 poles, by 11, and 49. (39) Divide 2019 acres, 3 roods, 29 perches, by 26. (40) Divide 117 years, 7 months, 26 days, 11 hours, 27 minutes, by 37.

PROMISCUOUS EXAMPLES.

(1) Of three numbers, the first is 215, the second 519, and the third is equal to the other two. What is the sum of

them all?

Ans. 1468. (2) The less of two sums of money is £40. and their difference £14. What is the greater sum, and the amount of both? Ans. £54. the greater, £94. the sum. (3) What number added to ten thousand and eighty-nine, will make the sum fifteen thousand and forty? Ans. 4951. (4) What is the difference between six dozen dozen, and half a dozen dozen; and what is their sum and product?

Ans. diff. 792, sum 936, product 62208.

(5) What difference is there between twice eight and fifty and twice fifty-eight, and what is their product?

Ans. 50 diff. 7656 product. (6) The greater of two numbers is 37 times 45, and their difference is 19 times 4: required their sum and product? Ans. 3254 sum, 2645685 product.

(7) A gentleman left his elder daughter £1500. more than the younger, whose fortune was 11 thousand, 11 hundred, and £11. Find the portion of the elder, and the amount of both. Ans. Elder's portion £13611. amount £25722. (8) The sum of two numbers is 360, the less is 144. What is their difference and their product?

Ans. 72 difference, 31104 product. (9) There are 2545 bullocks to be divided among 509 men. Required the number and the value of each man's share, supposing every bullock worth £9..14..6?

Ans. Each man had 5 bullocks, and £48..12..6. for his share. (10) How many cubic feet are contained in a room, the length of which is 24 feet, the breadth 14 feet, and the height 11 feet ?* Ans. 3696.

(11) A gentleman's garden containing 9625 square yards, is 35 yards broad: what is the length? Ans. 275 yards. (12) What sum added to the 43rd part of £4129. will make the total amount=£240? Ans. £137. (13) Divide 20s. among A, B, and C, so that A 2s. less than B, and C 2s. more than B.

.

may

have

Ans. A 4s. 8d. B 6s. 8d. and C 8s. 8d. (14) In an army consisting of 187 squadrons of horse, each 157 men, and 207 battalions of foot, each 560 men, how many effective soldiers are there, supposing that in 7 hospitals there are 473 sick? Ans. 144806.

(15) A tradesman gave his daughter, as a marriage portion, a scrutoire, containing 12 drawers; in each drawer were six divisions, and in each division there were £50. four crown pieces, and eight half-crown pieces. How much had she to her fortune? Ans. £3744.

(16) There are 1000 men in a regiment, of whom 50 are officers: how many privates are there to one officer? Ans. 19. (17) What number must 7847 be multiplied by, to produce

3013248?

Ans. 384.

* Multiply the three dimensions continually together.

(18) Suppose I pay eight guineas and half-a-crown for a quarter's rent, but am allowed 15s. for repairs; what does my apartment cost me annually, and how much in seven years? Ans. In one year, £31..2. In seven, £217..14.

(19) The quotient is 1083; the divisor 28604; and the remainder 1788: what is the dividend? Ans. 30979920.

(20) An assessment was made on a certain hundred, for the sum of £386..15..6. the amount of the damage done by a riotous assemblage. Four parishes paid £37..14..2. each; four hamlets £31..4..2. each; and four townships £18..12..6. each: how much was deficient? Ans. £36..12..2.

(21) An army consisting of 20,000 men, got a booty of £12,000; what was each man's share, if the whole were equally divided among them? Ans. 12s.

(22) A gentleman left by will, to his wife £4560;-to a public charity, £572..10;-to four nephews, £750..10. each; -to four nieces, £375..12..6. each;-to thirty poor housekeepers, 10 guineas each ;—and to his executors 150 guineas. What was the amount of his property? Ans. £10109..10.

(23) My purse and money, said Dick to Harry, are worth 12s. 8d. but the money is worth seven times the value of the purse: what did the purse contain? Ans: 11s. 1d.

(24) Supposing 20 to be the remainder of a division, 423 the quotient, and the divisor the sum of both, plus 19; what is the dividend? Ans. 195446. (25) A merchant bought two lots of tobacco, which weighed 12 cwt. 3 qrs. 15 lb. for £114..15..6; their difference in weight was 1 cwt. 2 qrs. 13 lb. and in price £7..15..6. quired their respective weights and value ?*

Re

Ans. Greater weight 7 cwt. 1 qr. value £61..5..6. Less weight 5 cwt. 2 qrs. 15 lb. value £53..10. (26) Divide 1000 crowns in such a manner among A, B, and C, that A may receive 129 crowns more than B, and B 178 less than C. Ans. A 360 crowns, B 231, C 409.

(27) If 103 guineas and 7s. be divided among 7 men, how many pounds sterling is the share of each? Ans. £15..10. (28) A certain person had 25 purses, each purse containing 12 guineas, a crown, and a moidore, how many pounds sterling had he in all? Ans. £355.

Add the difference to the sum, and divide by 2 for the greater; subtract the difference from the sum, and divide by 2 for the less.

C

(29) A gentleman, in his will, left £50. to the poor, and ordered that should be given to old men, each man to have 5s.- to old women, each woman to have 2s. 6d.—

to poor boys, each boy to have 1s.— to poor girls, each girl to have 9d. and the remainder to the person who distributed it: how many of each sort were there, and what remained for the person who distributed the money?

Ans. 66 men, 100 women, 200 boys, 222 girls;

£2..13..6. for the distributor. (30) A gentleman sent a tankard to his goldsmith, that weighed 50 oz. 8 dwts. to be made into spoons, each weighing 2 oz. 16 dwts. how many would he have? Ans. 18.

(31) A gentleman has sent to a silversmith 137 oz. 6 dwts. 9 gr. of silver, to be made into tankards of 17 oz. 15 dwts. 10 gr. each; spoons of 21 oz. 11 dwts. 13 gr. per dozen; salts, of 3 oz. 10 dwts. each; and forks, of 21 oz. 11 dwts. 13 gr. per dozen; and for every tankard to have one salt, a dozen spoons, and a dozen forks: what number of each will he have? Ans. Two of each sort, 8 oz. 9 dwts. 9 gr. over. (32) How many parcels of sugar of 16 lb. 2 oz. each, are there in 16 cwt. 1 qr. 15 lb.?

Ans. 113 parcels, and 12 lb. 14 oz. over. (33) In an arc of 7 signs, 14° 3′ 53′′, how many seconds? Ans. 806633".

(34) How many lbs. of lead would counterpoise a mass of bullion weighing 100 lbs. Troy ?* Ans. 82 lb. 4 oz. 92% dr.

(35) If an apothecary mixes together 1 lb. avoirdupois of white wax, 4 lbs. of spermaceti, and 12 lbs. of olive oil, how many ounces, apothecaries' weight, will the mass of ointment weigh, and how many masses of 3 drams each will it contain? Ans. the whole 247 oz. 784 dr. and 661 of 3 dr. each.

64

PROPORTION.

PROPORTION is either DIRECT, or INVERSE. It is commonly called the RULE OF THREE; there being always three numbers or terms given, two of which are terms of supposition; and the other is the term of demand: because it requires a fourth

* Bullion is the term denoting gold or silver in the mass. Lead is weighed by Avoirdupois weight. See the Table of COMPARISON OF WEIGHTS.

term to be found, in the same proportion to itself, as that which is between the other two.

GENERAL RULE FOR STATING THE QUESTION. Put the term of demand in the third place; that term of supposition which is of the same kind as the demand, the first; and the other, which is of the same kind as the required term, the second.*

Also, the terms being thus arranged, reduce the first and third (if necessary) into one name, and the second into the lowest denomination mentioned.

THE RULE OF THREE DIRECT

REQUIRES the fourth term to be greater than the second, when the third is greater than the first; or the fourth, to be less than the second, when the third is less than the first.

RULE. Multiply the second and third together, and divide their product by the first: the quotient will be the answer, in the same denomination as the second.†

The following methods of contracting the operations in the RULE OF THREE are highly important, and should never be lost sight of. 1. Let the first and third terms be reduced no lower than is necessary, to make them of the same denomination.

2. Let the dividing term and either (but not both) of the other terms be divided by any number that will divide them exactly; and use the quotients instead of the original numbers.

3. When it is conveniently practicable, work by Compound Multiplication and Division, instead of reducing the terms.

* Some modern authors prefer placing the term of demand the second, and that similar to the required term the third. This arrangement will answer the purpose equally well, observing that those of like kind must be reduced (if necessary) to the same name.

The following GENERAL RULE comprehends both the cases of DIRECT and INVERSE PROPORTION under one head; which is considered by many scientific men of the present day as a more systematic arrangement.

RULE. The question being stated, and the terms prepared, consider, from the nature of the case, whether the required term is to be greater or less than the second, or term of similar kind: if greater, multiply that similar to the answer by the greater of the other two, and divide the product by the less; if less, multiply it by the less and divide the product by the greater. In either case the quotient will be the term required, in the same denomination as the similar term.

NOTE. It is evident that the above Rule will answer generally, whether the term of demand is put in the second or third place.