17. The owner of an estate sold 240 acres of land and had 312 acres left how many acres had he at first?

18. Mr. James bought of Mr. Johnson two farms, one containing 250 acres, for which he paid 85 dollars per acre; the second containing 175 acres, for which he paid 70 dollars an acre; he then sold them both for 75 dollars an acre: did he make or lose, and how much?

19. A farmer has 279 dollars with which he wishes to buy cows at 25 dollars, sheep at 4 dollars, and pigs at 2 dollars apiece, of each an equal number: how many can he buy of each sort?

20. The sum of two numbers is 3475, and the smaller is 1162: what is the greater?

21. The difference between two numbers is 1475, and the greater number is 5760: what is the smaller?

22. If the product of two numbers is 346712, and one of the factors is 76: what is the other factor?

23. If the quotient is 482, and the dividend 135442: what is the divisor?

24. A gentleman bought a house for two thousand twentyfive dollars, and furnished it for seven hundred and six dollars; he paid at one time one thousand and ten dollars, and at another time twelve hundred and seven dollars: how much remained unpaid?

25. At a certain election the whole number of votes cast for two opposing candidates was 12672: the successful candidate received 316 majority: how many votes did each receive?

26. Mr. Place purchased 15 cows: he sold 9 of them for 35 dollars apiece, and the remainder for 32 dollars apiece, when he found that he had lost 123 dollars: how much did he pay apiece for the cows?

27. Mr. Gill, a drover, purchased 36 head of cattle at 64 dollars a head, and 88 sheep at 5 dollars a head; he sold the cattle at one-quarter advance and the sheep at one-fifth advance: how much did he receive for both lots?

28. Mr. Nelson supplied his farm with 4 yoke of oxen at 93 dollars a yoke; 4 plows at 11 dollars apiece; 8 horses at 97 dollars each; and agrees to pay for them in wheat at 1 dollar and a half per bushel: how many bushels must he

29. If a man's salary is 800 dollars a year and his expenses 425 dollars, how many years will elapse before he will be worth 10000 dollars, if he is worth 2500 dollars at the present time?

30. How long can 125 men subsist on an amount of food that will last 1 man 4500 days?

31. A speculator bought 512 barrels of flour for 3584 dollars and sold the same for 4608 dollars: how much did he gain per barrel ?

32. A merchant bought a hogshead of molasses containing 96 gallons at 35 cents per gallon; but 26 gallons leaked out, and he sold the remainder at 50 cents per gallon: did he gain or lose, and how much?

33. Two persons counting their money, together they had 342 dollars; but one had 28 dollars more than the other: how many had each ?

34. Mrs. Louisa Wilsie has 3 houses valued at 12530 dollars, 11324 dollars, and 9875 dollars: also a farm worth 6720 dollars. She had a daughter and 2 sons. To the daughter she gives one-third the value of the houses and one-fourth the value of the farm, and then divides the remainder equally among the boys: how much did each receive?

35. A person having a salary of 1500 dollars, saves at the end of the year 405 dollars: what were his average daily expenses, allowing 365 days to the year?

36. Mr. Bailey has 7 calves worth 4 dollars apiece, 9 sheep worth 3 dollars apiece, and a fine horse worth 175 dollars. He exchanges them for a yoke of oxen worth 125 dollars and a colt worth 65 dollars, and takes the balance in hogs at 8 dollars apiece: how many does he take?

37. Mr. Snooks, the tailor, bought of Mr. Squire, the merchant, 4 pieces of cloth; the first and second pieces each measured 45 yards, the third 47 yards, and the fourth 53 yards; for the whole he paid 760 dollars: what did he pay for 35 yards?

38. Mr. Jones has a farm of 250 acres, worth 125 dollars per acre, and offers to exchange with Mr. Cushing, whose farm contains 185 acres, provided Mr. Cushing will pay him 20150 dollars difference: what was Mr. Cushing's farm valued at per acre?

39. The volcano in the island of Bourbon, in 1796, threw out 45000000 cubic feet of lava: how long would it take 25 carts to carry it off, if each cart carried 12 loads a day, and 40 cubic feet at each load?

40. The income of the Bishop of Durham, in England, is 292 dollars a day; how many clergymen would this support in a salary of 730 dollars per annum?

41. The diameter of the earth is 7912 miles, and the diameter of the sun 112 times as great: what is the diameter of the sun?

42. By the census of 1850, the whole population of the United States was 23191876; the number of births for the previous year was 629444 and the number of deaths 324394: supposing the births to be the only source of increase, what was the population at the beginning of the previous year?

43. Mr. Sparks bought a third part of neighbor Spendthrift's farm for 2750 dollars. Mr. Spendthrift then sold half the remainder at an advance of 250 dollars, and then Mr. Sparks bought what was left at a further advance of 250 dollars: how much money did Mr. Sparks pay Mr. Spendthrift, and what did he get for his whole farm?

44. George Wilson bought 24 barrels of pork at 14 dollars a barrel; one-fourth of it proved damaged, and he sold it at half price, and the remainder he sold at an advance of 3 dollars a barrel: did he make or lose by the operation, and how much?

45. A miller bought 320 bushels of wheat for 576 dollars, and sold 256 bushels for 480 dollars: what did the remainder cost him per bushel?

46. A merchant bought 117 yards of cloth for 702 dollars, and sold 76 yards of it at the same price for which he bought it; what did the cloth sold amount to?

47. If 46 acres of land produce 2484 bushels of corn; how many bushels will 120 acres produce?

48. Mr. J. Williams goes into business with a capital of 25000 dollars; in the first year he gains 2000; in the second year 3500 dollars; in the third year 4000 dollars; he then invests the whole in a cargo of tea and doubles his money; he then took out his original capital and divided the residue equally among his 5 children: what was the portion of each?

UNITED STATES MONEY.

81. Numbers are collections of units of the same kind. In forming these collections, we first collect the lowest or primary units, until we reach a certain number ; we then change the unit and make a second collection, and after reaching a certain number we again change the unit, and so on.

In abstract numbers, we first collect the units 1 till we reach ten; we then change the unit, to 1 ten, and collect till we reach 10; we then change the unit to 100, and so on.

A SCALE expresses the relations between the orders of units, in any number. There are two kinds of scales, uniform and varying. In the abstract numbers, the scale is uniform, the units of the scale being 10, at every step.

82. United States money is the currency established by Congress, A.D. 1786. The names or denominations of its units are, Double Eagles, Eagles, Dollars, Dimes, Cents, and Mills.

The coins of the United States are of gold, silver, and copper, and are of the following denominations :

1. Gold: Double-eagle, eagle, half-eagle, three-dollars, quarter-eagle, dollar.

2. Silver Dollar, half-dollar, quarter-dollar, dime, halfdime, and three-cent piece.

3. Copper Cent, half-cent.

81. What are numbers? How are numbers formed? How are simple numbers formed? What is the scale? What is the primary unit in simple numbers?

83. It is seen, from the above table, that in United States money, the primary unit is 1 mill; the units of the scale, in passing from mills to cents, are 10. The second unit is 1

cent, and the units of the scale, in passing to dimes, are 10. The third unit is 1 dime, and the units of the scale in passing to dollars, are 10. The fourth unit is 1 dollar, and the units of the scale in passing to eagles, are 10. This scale is the

same as in simple numbers; therefore,

The units of United States money may be added, subtracted, multiplied, and divided, by the same rules that have already been given for simple numbers.

NUMERATION TABLE.

Tens of dollars or Eagles. Dollars.

Tens of cents or dimes.

Cents.

Mills.

57, is read 5 cents and 7 mills, or 57 mills. 164, 16 cents and 4 mills, or 164 mills.

62.120, 27.623,

- 62 dollars 12 cents and no mills.

27 dollars 62 cents and 3 mills. 4 0.041, - - 40 dollars 4 cents and 1 mill.

The period, or separatrix, is generally used to separate the cents from the dollars. Thus $67.256 is read 67 dollars 25 cents and 6 mills. Cents occupy the two first places on the right of the period, and mills the third.

United States money is read in dollars, cents and mills.

82. What is United States money? What are the names of its units? What are the coins of the United States? Which gold? Which silver? Which copper?

83. In United States money what is the primary unit? What is the scale in passing from one denomination to another? How does this compare with the scale in simple numbers ? What then follows? What is used to separate dollars from cents? How is United States money read?

84. What is reduction? How many kinds of reduction are there? Name them. How may cents be changed into mills? How may dol lars be changed into cents? How into mills?