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102. A goldsmith having 16 ingots of silver, each weighing

2 lb. 4 oz. which he made into bowls of 2 lb. 8 oz. tankards of 1 lb. 6 oz. salts of 10 oz. 10 dwt. and spoons of 1 oz. 18 dwt. and of each an equal number. Quere, that number?

Ans. 7 of each, 224 dwt. over. 103. In 73. 53.27. 15 grs. of ipecacuanha, how many doses of 16 grs. each, after deducting for waste 19 grains ?

Aris. 231 104. In 264 drams of metal, how many weights of 1 gr, 1 gr.

2 grs. 4 grs. 5 grs. 10 grs. 19.2.13.23.4 3.1 3. and

of each an equal number? Ans. 16 of each, 120 grs.over. 105. In 12880 lb. of sugar, how many hhds. each 11{cwt ?

Ans. 10. 106. In 507 cwt. of lead, how many fodder ?

26. 107. In 12 cwt. 3 qrs. 12 lb. of tea, how many canisters of 12 lb. each can be filled ?

Ans. 120. 108. In 1 hhd. of sugar, weighing net 8} cwt. how many parcels, each 1262 lb.

Ans. 7 parcels, 94{ lb. over. 109. In 2 tierces of tobacco, each weighing net 4 cwt. 3 qrs.

24 lb. how many parcels of 6 lb. 8 lb. 12 lb. and 16 lb.

and of each an equal number ? Ans. 26 of cach, 20 lb.over. 110. In 7 cwt. 3 qrs. 17 lb. of gun-powder, how many cartridges of 3 pound each ?

Ans. 295. To reduce great pounds into common, X by 3, and by 2.

To reduce common pounds to great, x by 2, and · by 3. 111. In 547 great pounds, how many common lb.! Ans. 8201 112. In 552 common pounds, how many great lb ? 368 113. In 16 miles, how many feet, inches and barley corns ?

Ans. 844 ft. 1013760 in. 3041280 b.c. 114. In 2280060 barley corns, how many miles ?

Ans. 11 m. 7 f. 38 p. 115. How many barley corns will reach round the terraqueous globe, which is 360 degrees, and each degree 693 miles ?

Ans. . 4755801600. 116. In running 150 miles, required the number of revolu

tions a wheel 18 feet 4 inches will make ? Ans. 43200. 117. In 21600 turns of a measuring wheel 18 feet, 4 inches in circumference, how many miles?

Ans. 75. 118. In 30 ells, English, 4 quarters, 3 nails, how many nails ?

Ans. 619, 119. In 569 nails, how many ells, Flemish ? Ans., 47 e.F. 19.1n. 1:20. In 12 pieces of cloth, each 20 ells, Flemish, how many ells English?

Ans. 144. 121. In 5625 yards of cloth, how many bales of 25 pieces

coch, and each piece 15 eUs, English ? Ans. 12.

122. In 64 acres of land, how many roods and poles ?

Ans. 256 r. 10240 p. 123. In 21760 poles, how many acres ?

136 124. In a field of 774 acres, how many shares of 270 perches each?

Ans. 458 and 180 poles over. 125. A farmer rents a plantation of 200 acres, of which he

is to till no more than 964 acres, how many poles are there in the remainder ?

Ans. 16560 126. In a log of timber that is 14 feet square, and 16 in length, how many solid inches and feet?

Ans.

62208 in. 36 ft. 127. In 317520 solid inches, how many cubic feet?

Ans. 183 ft. 9 in. 128. In 24 quarters of wheat, how many pecks and gallons ?

Ans. 768 pecks, 1536 gal. 129. In 3360 gallons of corn, how many quarters ?

Ans. 52 qrs. 4 bu. 130. In 40 chaldron of coals, how many bushels and pecks ?

Ans. 1440 bu. 5760 pks. 131. In 4762 bushels, how many chaldron of coals ?

Ans. 132 ch. 10 bu. 132. In 12 barrels of ale, how many gallons and pints ?

Ans.' 384 gal, 3072 pts. 133. In 1704 pints of ale, how many barrels ?

Ans. 6 bar. 21 gal. 134. In 6 barrels, 2 firkins, 7 gallons, of beer, how many gallons ?

Ans. 241. 135. In 4 tuns, 1 butt, 1 hhd. 49 gallons of beer, how many hhds. barrels and firkins, and of each an equal number?

Ans. 10 of each, and 85 gal.over. 136. In 12 tierces of wine, how many gallons and pints ?

Ans. 504 gal. 4032 pts. 137. In 6048 pints, how many tierces ?

Ans. 18. 138. In a tun of wine, how many quarts, pints and half

pints, and of each an equal number? Ans. 576. 139. In 1890 gallons of wine, how many pipes, puncheons, hogsheads artı tierces, and of each and equal number?

Ans. 6. 140. In a lunar month, or 27 days, 7 hours, 43 minutes, 5

seconds, how many seconds ? Ans. 2360585 sec. 141. How many days is it since the birth of our Saviour to

Christmas, 1808, allowing the year to be 365 days 6 hours ?

Ans. 660824. 142. In 17 score, how many dozens ?

28 doz. and 4 143. In 9} long hundreds, how many scores, dozens, and

half dozens, and of each an equal number? Ans. 30.

cts.

THE RULE OF THREE DIRECT. The Rule of Three Direct teaches by having three numbers given to find a fourth, which shall bear such proportion to the second as the third doth to the first; and is that in which more requires more, or less requires less.

RULE.-State the question by making that number which asks, the third term ; that which is of the same name or quality as the first term ; and that which is of the same name or quality with the answer required, the second term. Then multiply the second and third terms together, and divide the product by the first. The quotient will be the fourth term or answer, in the same name or denomination as the second term was left in.

Note-The first term is always known by the words if, or at; and the third term is also known by the words how much, or what will.

EXAMPLES. 1. If 4 lb. of tobacco 75 c. what will 28 lb. cost at that rate ?

16.

Ib. $ cts.

4 : 75 : : 28: 5 25 the answer. 2. If 75 cents buy 4 lb. of tobacco, how much will $5 25 c. buy ?

Ans. 28 lb. 3. If 28 lb. of tobacco cost $5 25 cents, how much can I buy for 75 cents ?

Ans. 4 lb. 4. Suppose $54 will buy 28 lb. of tobacco, 'what will 4 lb. of the same tobacco cost?

Ans. 75 cents. 5. If 19 dozen pair of stockings cost £76 19s. what cost 1 pair ?

Ans. 68. 9d. 6. If 1 pair of stockings cost 68. 9d. what cost 19 dozen pair?

Ans. £76 198. 7. What is the price of 239 eggs, when they are rated at 15 for a shilling?

Ans. 155. 113. 8. If a yard of cloth is worth 42 shillings, what is the worth of 5 pieces, each 19 yards ? Ans. £199 10s.

9. Suppose a ship to be valued at $2824 40 cents, what will of her cost ?

Ans. • $1059 15 cts. 10. Abraham had fine pears, 9 of which were worth 6 cents ; Billy had apples, 8 of which were worth 2 cents. Required the number of apples that Billy must give Abraham for 15 of his pears?

Ans. 40. 11. If a gentleman whose annual income is £1200, spend £21 a week: whether will he save or run in debt, and how much in a year?

Ans.

save £108. 12. Charles told Frederick, that his purse and money were worth £3 158. 61d. but that the money was worth six times as much as the purse. Pray how much was there in it?

Ans.

43 45. 9d.

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13. Two men depart from one place, the one goes north 35 miles a day, and the other south 43 miles a day, how far are they distant the 12th day after their departure ?

Ans. 936 miles. 14. Two men depart both from the same place, and travel the same road, the one 35 miles, and the other 43 miles eve. ry day. I demand how many miles they are distant the 12th day after their departure ?

Ans. 96 miles. 15. Admit that a cannon may be discharged 3 times with 9 lb. of powder; how many times will 7 cwt. 3 qrs. 17 lb. discharge the same gun?

Ans. 295 times. 16. How many yards of linen may be bought for £27 11e. whereof 7 yards cost £1 73. 24d. Ans.

152 yards. 17. If 3 paces of common steps of a certain person be equal to 2 yards ; how, many yards will 160 of his paces make?

Ans. 106 yds. 2 ft. 18. To how much amounts 172 pieces of lead, each weighing 3 cwt. 2 qrs. 173 lb. at £8 178. 6d. per fodder of 191 cwt ?

Ans.

£286 4s. 41d. 19. A person failing in trade, owes in all £997 ; at which time he has in money, goods and recoverabre-debts, 6420 Cs. 31d. ; now supposing these thine Idelivered to his creditors, how much will they get per po

Ans.

88. 7£d. 20. The circumference of the earth is about 25000 miles : at what rate per hour is a person at the middle of its surface carried round, one whole rotation being made in 23 hours 56 minutes ?

Ans. 1044 816 miles. 21. Having sold goods for £815 12s. how much must I remit to my employer after deducting 1} per cent commission ?

Ans. £803 7s. 3168.1. 22. A captain of a ship being provided with 24000 lb. of bread for 200 seamen, of which each man eats 4 lb. per week, how long will the bread last ?

Ans. 30 weeks. 23. Two persons A. and B. depart from Albany for Phila. delphia, but A. sets off 3 days before B. and travels 30 miles

a day: B. follows after him the same road and travels 50 Emiles I demand in how many days, and after how many miles travel will B. overtake A.?

Ans. 4 days, and 225 miles. 24. As I was beating on the forest grounds,

Up starts a hare before iny two grey-hounds, ;
The dogs, being light of foot, did fairly run,
Unto her fifteen rods, just twenty-one.
The distance that she started up before
Was fourscore, sixteen rods just, and no more ;
Now this I'd have you uro me declare,
How far they run before they caught the hare?

1936 rods.

25. A merchant at New-York imports from Constantinople, goods which cost $4600, the freight from thence to NewYork, $225, porterage $17 35 cents, duties and fees $234 75 cents, storage $23 12 cents, and he would gain $2125 by the bargain. I demand how much 24 of the said goods will amount to?

Ans. $2709 45 c. 92. m. 26. A gentleman has £510 8s. 4d. per annum.

I demand how much he may spend per day, so as to be able to lay up £115 yearly?

Ans. £1 18. 8d. 27. Bought 30 hogs for £70, and sold them for £80, now if they had cost £80, how should they have been sold to have gained after the same rate ?

Ans. £91 88. 6694. 28. If 60 gallons of water, in 1 hour's time, fall into a cis. tern containing 200 gallons, and by a pipe in the same cistern there runs out 45 gallons in an hour, in what time will it be filled?

Ans. 13 ho. 20 min. 29. A merchant failing in trade, paid 49 cents in the dollar, to his creditors, to whom he was indebted $11573. Pray what sum did he pay them? Ans. $5670 77 cts.

30. In £460 how many thillings, six-pences, four-pences, two-pences and pence, ay each an equal number?

Ans. 4416. 31. A drover having bougit 64 fat oxen at $50 a head, the expence of driving to market is $20, for butchering $33}, of salt $265, of barrels and storage $50, and he would gain $654 on the whole, what will be the

price of 27 of said oxen, in barrels ?.

Ans. $1687 50 cts. 32. If from a rod of 6 feet long, the shadow 10 is made, I ask the steeple’s height in yards, that's 90 feet in shade!

Ans. 18. 33. An oilman bought 3 tuns of oil at £50 11s. 4d. per tun; by some accident it leaked out 85 gallons ; but he is minded to sell it again so as to be free from loss. How must he sell it per gallon?

Ans. 4s. 6174d. 34. If £100 gain £7 interest in 12 months ; what will £63 gain in the same time?

Ans. £4 8s. 20. fiori 35. If 8 lb. of pepper cost 14s. what will 7 cwt. 3 qrs. 416. cost?

Ans. £77 39. 6d. 36. A certain usurer put out $75 for 12 months, and received for principal and interest, $81. Required the rate of interest ?

Ans. 8 per cent. 37. A bankrupt's effects amount to 118. 71d. per pound, what will B. get, to whom he is owing £300 ?

Ans.

£174 7s. 6d. 38. If a merchant in selling tea at 88. per lb. gain 12 per cent. what will he gain per cent. in seiling the same tea at 95. per lb ?

Ans. 26 per cent.

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