ANALYSIS.

47. Perform the questions in this article by Analysis; that is, first find the value of a unit, or single thing, of the unknown quantity, and then find the value of the whole number required.

The pupil has already had some exercises in analysis in preceding articles. For instance, questions 7 to 15 in Art. 34, 31 to 46 in Art. 44, &c., are examples of analysis. But as this mode of solving questions is so commonly practised by business men, and is so interesting to the pupil, and, at the same time, so well fitted to discipline his mind, and to prepare him better to understand the more difficult parts of arithmetic, the subject of analysis should have a prominent place in a text-book on Arithmetic.

1. If 4 lb. of veal cost 28 cts., what will 8 lb. cost?

Solution. Since 4 lb. cost 28 cts., 1 lb. will cost of 28 cts., or 7 cts. If 1 lb. costs 7 cts., 8 lb. will cost 8 times as much; 8 times 7 cts. = 56 cts.; therefore, if 4 lb. of veal cost 28 cts., 8 lb. will cost 56 cts. 2. If 5 lb. of lamb cost 20 cts., what will 8 lb. cost? 10 lb.? 12 lb.?

3. If 7 yd. of cloth cost $35, what will 8 yd. cost? 4 yd.? 31 yd.? 10 yd.?

4. If 6 lb. of coffee cost 66 cts., what will 3 lb. cost? 34 lb.? 5 lb.? 84 lb.?

If 1 lb. cost 11 cts., 3 lb. will cost 3 times as much. 3 times 11 are 33; of 11 is 5, which added to 33 makes 384; therefore, if 1 lb. costs 11 cts., 3 lb. will cost 38 cts.

5. If 7 horses eat 36 bushels of oats in a week, how many bushels will 3 horses eat? 5 horses? 6 horses? 10 horses?

6. If a man travels 26 miles in 6 hours, how far will he travel in 2 hours? 5 hours? 8 hours?

7. Bought 5 yards of ribbon for 42 cents; what are 3 yards worth? 8 yards? 10 yards? 12 yards?

8. If a man earns 50 shillings in 6 days, how much will he earn in 5 days? In 8 days? In 7 days? In 12 days?

9. If 3 men eat a bushel of potatoes in 20 days, how long will they last 5 men? 8 men? 10 men? Since the bushel will last 3 men 20 days, it will last 1 man 3 times as long, or 60 days. If it last 1 man 60 days, it will last 5 men as long, or 12 days. Therefore, &c.

10. If 8 men build a wall in 7 days, how long will it take 3 men to build it? 5 men? 7 men? 10 men? 12 men?

11. If 7 men do a piece of work in 45 days, in what time will 15 men do it?

12. If $100 worth of provisions will last 5 men 75 days, how long will they last 12 men? 18 men? 37 men?

13. If a railroad car runs 140 miles in 7 hours, how far will it run in 8 hours? In 7 hours? In 25 hours?

14. If 35 barrels of apples cost $48, how much will 3 barrels cost? 8 barrels? 27 barrels ?

15. A drover bought 250 sheep for $375; how much would 75 sheep cost?

16. A merchant bought 25 barrels of flour for $162.50; what are 8 barrels worth?

17. If 151⁄2 tons of coal cost $95, what is the cost of 1 ton? 6 tons?

153—95. If 22 of a ton cost $95, † of a ton will cost of $95, or $1.

18. Bought 33 cords of wood for $27; what was it per cord? 19. Gave $43 for 5g yards of broadcloth; what was it per yard?

20. How many times will 95 contain 15g? 21. How many times will 27 contain 33? 22. How many times will 43 contain 53 ?

23. A farmer sold 63 bushels of potatoes for $3.24; how much did he get per bushel? What would 25 bushels come to at that price?

24. How many times will 324 contain 63? 7?

25. The farmer in the last example paid $1.77 for a keg of molasses, containing 73 gallons; what was the price per gallon?

26. How many times will 354 contain 7?

13?

27. If 25 gallons 2 quarts of wine cost $33.15, what was the price per gallon? What would 81 gallons come to at that price?

I

28. Paid $2.70 for 3 bushels of Indian meal; what must pay for 5 bushels at that rate?

29. How many cows at $25.50 apiece can be bought for $433.50?

TO THE TEACHER. If the pupil is a beginner on the slate, it may he well for him to review all the preceding articles from the beginning, performing all the examples, whether marked I. or II. He will in this way acquire a facility in performing the elementary processes which he cannot so readily acquire by going forward.

SECTION VI.-COMPOUND NUMBERS.

TABLES OF MONEY, Weights and Measures.

48. Federal Money. (Art. 15.)

Federal Money is the national currency of the United States. Its unit is the dollar. The coins are of gold, silver, and copper. The Gold coins are the double eagle,* eagle, halfeagle, quarter-eagle, and the dollar.* The Silver coins are the dollar, half-dollar, quarter-dollar, dime, half-dime. The Copper coins are the cent and half cent.

NOTE 1. If any quantity of gold be divided into 24 equal parts, each part is called a carat. The purity of gold is indicated in this manner. If the metal is pure, it is said to be 24 carats fine. If there are 22 parts of the pure metal mixed with 2 parts of silver or other baser metal, it is said to be 22 carats fine. Gold 18 carats fine has 18 parts pure gold and 6 parts alloy, that is, 6 parts of a baser metal.

2. The standard of the gold coin in the United States is 22 carats of gold, 1 of silver, and 1 of copper. The standard for silver coins is 1489 parts of pure silver to 179 of pure copper. The copper coins

are pure copper.

3. The eagle weighs 270 grains; the dollar, 416 grains; the cent, 11 pennyweights.

English Money is the national currency of Great Britain. It was the currency of the United States till the establishment of Federal Money in 1786, and is partially used here at present. Its unit is the pound, (£.)

* The double eagle and the gold dollar were introduced by act of Congress, February, 1849.

=

d.

gr.

1=20-240= 960

=

=

£1,

NOTE 1. The gold coins of Great Britain are the sovereign and the half-sovereign 10s. The silver coins are the crown = 5s., the half-crown = 2s. 6d., the shilling, and the sixpence. 2. 1 guinea = 21 shillings; its value is $5.07. The exchange value of the pound is $4.44. Its legal value at the mint is $4.866. At the custom-house it is received in payment of duties at $4.84. See Art. 122.

3. The standard gold coin of Great Britain is 22 parts of pure gold and 2 parts of pure copper. The silver coin is 224 pure silver and 18 of copper.

50. French Money.

100 centimes = 1 franc = $0.18%.

51. Troy Weight.

Troy Weight is used in weighing gold, silver, platina, jewels, and some liquids. Its unit is the pound, (lb.;) the standard of which in the U. S. is the weight of 22.794377 cubic inches of distilled water weighed in air. The pound Troy is the standard of weight in the United States.

1 pound

1 ounce

12 ounces,

(oz.) | 1 gr. = 24 of a dwt. 20 pennyweights, (dwt.) 1 dwt. =

of an oz.

1 pennyweight=24 grains,

(gr.) 1 oz.

of a lb.

Apothecaries' Weight is used in mixing medicines. Drugs are, however, bought and sold by Avoirdupois Weight. The pound, ounce, and grain, are the same as in Troy Weight.

* 1qr. is often written d.; 2qr. is written d.; 3qr. is ‡d.; 8d. 3qr. is 84d., &c.

Avoirdupois Weight is used in weighing most kinds of merchandise, and all the metals, except those mentioned in Troy Weight.

T. crot. qr.

1=20=80=2240-35840-573440

1=4=112= 1792= 28672

=

NOTE 1. The Avoirdupois pound of the United States is determined from the Troy pound. 1 lb. Troy: 5760 grains. 1 lb. Avoirdupois 7000 grains Troy. 1 oz. Avoirdupois contains 437 grains. 1 dr. = 27 grains. The lb. Avoirdupois is of the lb. Troy.

=

2. By a law of the United States the hundred weight is fixed at 100 lb. The ton of 2240 lb., the cwt. of 112 lb., and the qr. of 28 lb., are seldom used, either among merchants or at the custom-house, except in weighing hemp and dye-woods on first delivery, and coal at the mines and on first delivery; the ton of 2000 lb. and the hundred weight of 100 lb. being almost universally used. In invoices of goods from England which are sold by weight, the cwt. is estimated at 112 lb. Fish is bought by the quintal of 112 lb.

3. Gross weight is the weight of goods with the bags, casks, or boxes, which contain them. Net weight is the weight of the goods only.

54. Long Measure.

Long Measure is frequently called linear or lineal measure. It is used in measuring distances, as lengths, breadths, depths and heights.