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cwt. must he sell it in order to gain 5 per cent. and at what rate a lb. in order to gain 10 per cent. ?

Ans $10 1ct. 7m. t a cwt. and 9cts. 3m+ a lb. 22. Admitting the Hudson river to be 1000 feet broad, and 10 feet deep, and to run at the rate of 4 miles in an hour, in what time will it discharge a cubic mile of water (reckoning 5000 feet to the mile) into the sea ?

Ans. 26 days, 1 hour. 23. If A can do a piece of work alone in 8 days, B in 12 days and C in 16 days; in what time will all three finish it working together?

Ans. 39 days. First, Suppose the work to be divided into 48 parts.

days. days. parts. parts. Then say as 8:1:: 48 : 6=the num. that A can do in 1 day 12 : 1 :: 48 : 45

B do. 16 : 1 :: 48 3= do. C do.

13 the number of parts performed

by all three in one day.
parts. parts. day.
Again As

13:
48

3,5 day. Ans. Nie-In quins of this kind, suppose the work to consist of any number of pajis dat may be divided without reminders, by the different times in which the different persons are to perform the work, and proceed agreeably to the tenor of the question

24 A and B together can build a boat in 20 days; with the assistance of C, they can do it in 12; in what time would C do it by himself ?

Ans. 30 days. 25. A can do a piece of work alone in 13 days, and A and B together in 8 days; in what time can B do it alone? Ans. 209 days.

26. A, B, and C, can complete a piece of work in 15 days, A can do it alone in 30 days, and B in 40; in what time can C do it by himself?

Ans. 120 days. 27. In a certain orchard } of the trees bear apples, į pears, } plums, 60 of them peaches, and 40 cherries; how many trees are in the orchard ?

Ans. 1200. 28. A person, willing to distribute some money among a number of beggars, wanted Scts. to give them 3cts. a piece ; he therefore give each 2cts. and had 3cts. left, how many beggars were there?

Ans. 11. 29. A guardian paid his ward $3500, for $2500 which he had held in his possession 8 years'; what rate of interest did he allow him?

Ans. 5 per cent. 30. A stone is 4 feet 6 inches long, 2 feet 9 inches broad, and 3 feet 4 inches thick, how many solid feet does it contain ?

Ans. 41 feet 3 inches. 31. A ro m, 30ft. Jong, and 18ft. wide, is to be covered with painted cloch, how many yards a wide will cover it? Ans. 80yd.

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year?

32. If I buy 100 yards of ribbon, at 3 yards for a shilling, and 100 more at 2 yards for a shilling, and sell it at the rate of 5 yards for 2 shillings, do I gain or lose, and how much? Ans. lose 3s. 4d.

33. There is a mast or pole, į of its length stands in the ground, 12 feet of it in the water, and of its length in the air, or above water; how much is the whole length ? Ans. 216 feet.

34 The hour and minute hands of a watch are exactly together at 12 o'clock, when are they next together ?

The velocities of the two hands of a watch or clock, are to each other, as 12 to 1 ; therefore the difference of velocities is 12 1=-11. As 11 12x1

si
1 :
5 )

Ans. &c.
12 X 2

2 10 54 0 35. A person being asked the hour of the day, said the time past noon is equal to of the time till midnight ; what was the time ?

Ans. 20 minutes past 5. 36. If the earth be 360 degrees in circumference, and each degree 69} miles, how long would a man be in travelling round it who should travel 20 miles each day, reckoning 365 days in a

Ans. 3 years 155] days. 37. At the close of the American war the British government owed £280,000,000 and the pound sterling contains 3oz. 17dwt. 10yr. of silver; I demand the number of tons Avoirdupois, 7000 grains Troy being equal to one pound Avoirdupois; I likewise wish to know how long a string of wagons it would take to carry the whole, a ton at a load, and 3 rods apart ?

Wt. 33178T, 11cwt. Iqr. 20lb. Ans.

Distance 311 miles, 14rods. 38. A and B traded together; A put in $320 for 5 months, B $460 for 3 months, and they gained $100 ; what was each dian's share of the gain ?

A's share is $53 69cts. 10. + Ans.

is $46 30cts. 8m. + 39 Shipped to Jamaica 550 pair of stockings, at $1 40cts. a pair, and 460 yards of stuffs at 14cts. a yard ; in return for which I have received 46cwt. 3qr. of sugar, at $3 6cts. a cwtand 1570lb. of indigo, at 29cts. a lb. ; what remains due to me?

Ans. $236 4cts. 5m. 40. The accounts of a certain school are as follows ; viz: it of the boys learn geometry, learn grammar, i learn arithmetic, a learn to write, and 9 learn to read ; what number is there of each ?

5 learn geometry, 30

{

B's

Ans. Sarlittameteo net writing, and 9 reading

.

41. A lets B have a hogshead of sugar weighing 18cwt. worth $5, for $7 the cwt. ; of which he is to pay in cash ; B has paa per worth $2 the ream, which he gives Á for the rest of his set

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gar at $2} the ream ; which gained the most by the bargain

Ans. A by $19 20cts. 42. A stationer sold quills at 11s. a thousand, by which he eleared of the money ; but growing scarce, he raised them to 13s. 6d. a thousand ; what did he gain per cent from the prime cost by the latter price?

Ans. £96 75. 330. 43. A man gave to bis three sons all his estate in money; viz. to F half, wanting $50, to G one third, and to H the rest, which was 10 less than the share of G; I demand the sum given, and each man's part ? Ans. The sum given was $360 whereof F had

$130, G $120, and H $110. 44. A gentleman divided his fortune among bis three sons, giva ing A 19 as often as B £5 and to C but £3 as often as B £7 and yet C's dividend was £2584 ; what was the whole estate ?

Ans. £19466 2s. 8d. 45. A father left his two children, John and James (John 11 and James 16 years old) $10000 to be divided so that each share, being put to interest at 7 per cent. might amount to equal sums when they should be respectively 21 years of age. Required the shares.

John's share $442671. Ans.

James' share $557341 46. What is the difference between six dozen dozen, and a balf a dozen dozen ?

Ans. 792. 47. Three persons purchased together a ship, toward the payment of which A advanced and B of the value, and C £200, how much paid A and B, and what part of the vessel had C?

Ans. A £9011, B £11671, and C 31 part. 48. Laid out in a lot of muslin, £480 11s. upon examination of which, 2 parts in 7 proved damaged ; so that I could make but 5s. 6d. a yard of the same, and by so doing, I lost £49 6s. by it; at what rate an ell English, am I to part with the undamaged mus. lin to make up said loss?

Ans. 12s. 3. 49. A water tub bolds 147 gallons ; the pipe usually brings in 14 gallons in 9 minutes, the tap discharges at a medium 40 gal. lons in 31 minutes ; now, supposing the tap to be carelessly left open, and the water to be turned on at 2 o'clock in the morning; a servant at 5 finding the water running, shuts the tap, and is solicitous to know in what time the tub will be filled after this accident. Ans. the tub will be full at 3min. 48+sec. after 6.

50 Twenty knights, 30 merchants, 24 lawyers, and 24 citizens, spent at a dinner, £64 which sum was divided

among

them in such a manner that 4 knights paid as much as 5 merchants ; 10 merchants as much as 16 lawyers, and 8 lawyers as much as 12 citizens ; the question is to know the sum of money paid by all the knights s also by the merchants, lawyers, and citizens?

Ans 20 knights paid £20, the 30 merchants £24, the

24 lawyers £12, and the 24 citizens £8. 51. The yearly interest of Harriet’s money, at 6 per cent. ex. ceeds z' of the principal by a £100 and she does not intend to marry any man who is not scholar enough to tell her fortune ; pray what is it?

Ans. £10000. 52. A gentleman left his son a fortune ; il of which he spent in 3 months ; of of the remainder lasted him 9 months longer, when he had only £537 left; what did the father bequeath him?

Ans. 32082 185. 27.d. 53. There are three horses, belonging to different men, employed to draw a load from Poughkeepsie to Hartford for 35 dollars, A and B are supposed to do of the work, A and Cain and B and C of it. They are paid proportionally ; please to divide their

pay
for them as it should be.

(A $13 79+ Ans. B 45+

C - 14 75+ 54. A hare starts 12 rods before a haunt'; but is not perceived by him until she has been up 45 seconds ; she scuds away at the rate of 10 miles an hour, and the dog on view, makes after, at the rate of 16' miles an hour : how long will the course hold, and what space will be run over, from the spot where the dog started!

Distance 2288 feet.

Time 971 seconds. 55. There are two columns in the ruins of Persepolis left standing upright; one is 64 feet above the plain, the other fifty. Between these, in a right line stands an ancient statue, the head whereof is 97 feet from the summit of the higher, and 86 feet from the top of the lower column, and the distance between the lower column and the centre of the statue's base is 76 feet; required the distance between the top of the columns. Ans. If the statue be lower than the columns then the distano

between their tops will be 157 + feet. But if the statue

be higher, then their distance will be 169.95+ feet. 56. Hiero, king of Sicily, ordered his jeweller to make him e crown, containing 63 ounces of gold. The workman thought that substituting part silver was only a proper perquisite ; which taking air, Archimedes was appointed to examine it; who, on putting it into a vessel of water, found it raised the fluid 8.2245 cubic inches : and having discovered that the inch of gold weighed 10.36 ounces, and that of silver but 5.85 ounces, he found by calculation what part of the king's gold had been changed. Re.

process, and inform us what part of it was gold and what silver

34oz. 3dwt. 22 gr. gold. Ans.

280x. 16dwt, 1/gr. silver

Ans.

peat the

TABLE OF CONTENTS,

Page 13

25

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Expiration of Characten Page 4 | Foreigo Exchange

Nuneration

5 A Table of monies of different nations ih

Simple Addition

6 Questions in Interest, &e.

125

Simple Subtraction

9 Proiniscuous Questions to Exercise the

Simple Multiplication

10 learner in the foregoing rules

124

Simple Division

14 Mensuration

138

Supplement to Multiplication

18 Gauging

Questions in the Simple Rules

19
Federal Money Tables, Addition of Fede-

PART II.
ral Money

22

Subtraction of Federal Money

24 | Vuger Fractions. Reduction of Vulgas

Multiplication of Federal Money

Fractions
Division of Federal Money
27 Addition of Vulgar Fractions

146
Tables of Weights and Measures, &c. 29 Subtraction of Vulgar Fractions

147

Time

31 Multiplication of Vulgar Fractions ib.

Circular Motion

32 Division of Vulgar Fractions

149

Compound Addition

ib. The Single Rule of Three in Vulgar Frac-

Compound Subtraction

37 tions

Compound Multiplication

42 Double Role of Three in Vulgar Frac-

Compound Division

tions

130

Questions in the Compound Rule

52 Decimal Fractions

151

Reduction

54 Addition of Decimals

152

A table of coins which pass current in the Subtraction of Decimals

Sb.
United States of Norih America, with Multiplication of Decimals

ib.
their sterling and Federal value 62 Division of Decimals

154

Changing of Currencies

63 Reduction of Decimals

156

Vulgar Fractions

66 Single Rule of Three in Decimals

158

$i zle Rule of Three Direet

70 Double Rule of Three in Decimals 158
Invenge

Questions in Vulgar and Decimal Frae-

Pracice

78 tions

Tare and Tret
05 Alligation

162

Double Rule of Three

90 Single Position

166

Questions in Redaction, &c.

93 Double Position

167

Questions in Practice, &c.

94 Tovolution, or the Raising of Powers 169

Simple Interest

95 Square Root

170

Insurance, Commission and Brokage 108 Cube Root

178

Compound Interest

109 General Rule for extracting the Roots of

Discount

110 all powers

175

Equation

111 Arithmetical Progression

176

Barter

113 Geometrical Progression

178

Logs and Gaio

114 Permutation, and Combination

181

Single Fellowship

117 Questions in Alligation, Position, &c. 282

Compound Fellowship

119 Compound laterest by Decimals

189

Exchange

120 Duodecimals, and Multiplication of Duo-

A table exhibiting the value of a dollar in decimals

18$
each of the United States, with practi Promiscuous Questions to exercise the
eal theorems for exchanging the curren learner in the foregoing rules

of either into that of any other

160

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