1 In 6 signs of the zodiac, how many minutes?

answer 10800 2 How many seconds are there in one complete revolution of any planet ? answer 1296000

Application.

1 In 400 quarter dollars how many pounds? ans. 377. 10s. 2 How many marks, each 13s. 4d. are in 496l. 13s. 4d. P answer 745 3 How many English guineas are equal in value to 1200 moidores ? answer 1620 4 How many ducatoons, of 5s. 6d. each, are equal to 476 pieces, at 48. 7d. each ? answer 393 duc. 3s. 9d. 5 By what must 6l. 17s. 3d. be multiplied, to produce a product of 123l. 11s. 3d. P

answer 18 6 How many plates, of 12 ounces each, may be manufac- › tured out of 8 ingots of silver, each 36 ounces? answer 24 7 If a ship's cargo be 250 pipes, 130 hogsheads, and 150 half ditto; how many gallons in all? And allowing every pint to be a pound, what burden was the ship of? answer 44415 gallons, 1587. 120. 2qr. 8 What number of canisters, each to hold 38lb. may be filled from 28 chests of tea, each 2C. 1qr. 14lb. ? answer 196 9 How many parcels of 6lb. 8lb. 12lb. and 16lb. can a grocer have out of two hogsheads of tobacco, each weighing neat 4C. 3qr. 24lb. and to have of each a like number? answer 26 of each, and 2016. 10 How many barley corns would reach round the terrestrial globe, which is 360 degrees, and each degree 691 miles ? answer 4755801600 barley corns 11 how many boxes, each to hold 24lb. may be filled out of two hogsheads of tobacco, each containing 7C. 2qr.?

answer 70

12 Received from Jamaica 56 hogsheads of sugar, each 12C. 1gr. 10lb. (100lb. being their hundred weight) how many hundred weight here, of 112lb. ? answer 617 C. 2gr.

13 Imported from Rotterdam 46 bales of cloth, each containing 24 pieces, and each piece 42 ells Flemish; how many yards were therein ? answer 34776 yards 14 How many steps of 2ft. 8in. 1b.c. will a man take in walking 7M. 1fur. 94yds.?

answer 13923+ 15 A carriage wheel is 17ft. 2in. 1b.c. in circumference, and turns 12898 times; the distance is required ?

answer 42+miles 16 How many seconds of time have passed since the creation of the world, including the year 1790 ?

answer 182844734400 seconds 17 If 2yds. 3qrs. of cloth will make a coat, lyd. 1gr. a waistcoat, and lyd. 1qr. 2na. a pair of breeches; what number of yards will it take to make complete suits for answer 2418yds. 3qrs. 18 How many rings, each weighing 5dwt. 7gr. may be made of 3lb. 7oz. 16dwt. 2gr. of gold ?

450 men?

T

answer 158

THE SINGLE RULE OF THREE.

HE Single Rule of Three is that wherein three numbers, or terms, are given, two of which are of one kind, to find a fourth proportional number of the same name with the other given term; and this consists of two proportions, viz. direct and inverse.

RULE for Stating, &c.

Of the two similar terms, set that in the first place which implies the supposition, that of the same kind with the term sought in the second place, and that on which the demand lies in the third. If the first and third be not of one denomination, reduce both to the lowest in either, and the second to its lowest given denomination; then consider whether the proportion be direct or inverse.

DIRECT PROPORTION.

Direct proportion is that wherein the third term is greater than the first, and requires the fourth term to be greater than the second; or the third less than the first, and requires the fourth to be less than the second;

For, as often as the third term is greater or less than the first, so many times will the fourth be greater or less than the second. Thus,

As

yds. dols. yds. dols.

69 18 more requiring more

{20:40:9: 10 less requiring less

RULE.

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 with the second. PROOF.

Invert the question, beginning with the answer; and the result will be the first term; thus the preceding: dol. yds. dols. yds.

As

{

Note. The operation may frequently be contracted by dividing the dividing term, and either of the other two one by the other; or by any number that will divide them both without remainder, and using their quotients in their stead; cancelling the figure so contracted, as denoted by this dash in the two subsequent examples.

Thus, If 24 yards cost 60s. what are 8 yards worth?

Yds. s. yd.

As 24: 60 :: 8

8 20s. answer.

That is, 24-8= 3

12)

Ás 24: 60 :: 8

5

8

2)40

20s. answer.

answer £.13 12

2 If 8 yards of cloth cost 3 dols. 20 cts. what will 96 yards come to ?

3 How many yards of cloth may be 40cts. when 8 yards cost 3 dol. 20cts. ? 4 What will 9 yards of cambric cost, 16s. for 72 yards?

per

answer 38,40 bought for $8dol. answer 96 yards at the rate of 441. answer 51. 12s.

5 If 96lb. of sugar cost 9dol. 60cts. what is it per lb. ?

answer 10cts.

6 What is the value of 1 hundred weight of sugar, at 8d. lb. ? answer 31. 14s. 8d.

7 At 15d. per lb. what is loaf sugar per hundred weight?

answer 71.

8 What is the price of a barrel of beer, at 16d. per gallon ? answer 21. 2s. 9 If 19 dozen pair of hose cost 136dol. 80cts. what is that per pair?. answer 60cts. 10 Sold three hundred weight of tobacco, at 20cts. per lb. what is the amount? answer 67,20 11 If one hundred weight of iron be worth 11. 8s. what is the value of 33C. 1qr. 22lb. ?

answer 461. 16s. 6d. 12 Bought 12 pieces of cloth, each 12 yards, at 1 dol. 40cts. per yard; what come they to? answer 201,60 13 If 360z. 10dwt. of silver be worth 91. 2s. 6d. what is that per ounce ?

answer 5s.

14 When a bankrupt compounds with his creditors, at 70cts. in the dollar; what is the merchant's quota, to whom he owes 1000dols. ? answer 700dols. 15 What is tobacco an ounce, when 17€. 3qr. 17lb. sell for 1331. 13s. 4d. P

answer id.

16 What

16 What quantity of sugar will 237. 10s. buy, at 26s. 8d. per hundred weight? answer 17C. 2qr. 14lb. 17 What do 518lb. of tea come to, if 90lb. cost 181. and what is it per pound? answer 103l. 12s. at 4s. per lh. 18 If 17 T. 12C. of iron cost 440 dollars, what is that for two hundred weight?

answer 2,50 19 If a man's daily income be 2 dols. 40cts. how much is that per annum?

20 Bought 14 bags of hops, each 48 English guineas; what was the weight in Pennsylvania currency?

answer 876 dols. containing 546lb. for value of 1 hundred answer 11. 4s. 7d.t

21 What sum will pay for 3 casks of brandy, containing 58,62, and 65 gallons, at 89 cents per gallon?

answer 165 dollars 9 cents 5 mills. 22 What will 4 pieces of cloth come to, containing 23, 24, 25, and 27 yards, at 72 cents per yard? answer 71,28 23 Bought four pieces of linen, two of which contained 26 yards each, and each of the others 234 yards; what did they come to, at 44 cents per yard? answer 44,22

24 A draper bought 242 yards of broad cloth for 2541. 10s.; for 86 yards of which he gave 21s. 4d. per yard; what was the price per yard of the remainder? answer 20s. 10d.4

25 What must be paid for 53 ells English 1qr, of Holland, at the rate of 7s. 9d. per yard? ans. 251. 18s. 1d. 26 What quantity of sugar may be bought for 261. 10s. 4d. when the price of 43C. 2qr. is 159l. 2s.

answer 7C. 1gr.

27 A person failing in trade, owes 9777. and the inventory of his effects amounts to but 4201. 6s. 3d.4; how much will this produce per pound to his creditors? answer 8s. 7d.

28 What must be given for a piece of silver weighing 7316. 5oz. 15dwt. at 5s. 9d. per ounce ? answer 2531. 10s. Od. 29 Bought 2 casks of raisins, each weighing SC. 1gr. 7lb. neat; what will they cost, at 21. 6s. 6d. per hundred, weight? answer 231. 2s. 1d. 30 What will a tax upon 765l. 15s. be, at the rate of 38. 6d. per pound ? answer 1831. 13s. 1d. 31 How many ells English of Holland may be bought for 257, 18s. 1d., at 7s. 9d. per yard? 32 What will 1gr. ina. of velvet cost, at 18s. fd. per yard?

F

answer 53 E. 1qr.

answer 5s. 9d. 1gr. 33 A