you 36. If you had 118 dollars, how many hats could pay for, at 5 dollars apiece; and what number of dollars would you have left? 37. Suppose a drover has 2130 dollars; how many oxen can he pay for, at 47 dollars apiece; and how many dollars will he have left? 38. In 668 360 yards of cloth, how many pieces, and how many bales; there being 35 yards in each piece, and 56 pieces in each bale? 39. If 4810 dollars be shared equally among 130 men, how much will each man receive? 40. A farmer planted 2072 trees in 14 equal rows. How many did he plant in a row? 41. A gentleman wishes to spend 136 days in performing a journey of 3264 miles. How many miles must he travel each day? 42. If a man whose property is valued at 21 148 dolars be worth 17 times as much as his neighbor, how much is his neighbor worth? RETROSPECTIVE OBSERVATIONS. In the course of the last four chapters, you have practised four kinds of operations on numbers: viz. Addition, Subtraction, Multiplication, and Division. These operations should be perfectly understood-the effect of each should be distinctly perceived; for, it is on their proper application, that the solution of all questions in arithmetic depends. Addition is the operation by which two or more numbers are united in one sum. Subtraction is the operation by which the difference between two numbers is found. Multiplication is the operation by which a number is produced, equal to as many times one given number, as there are units in another given number. Division is the operation by which we find how many times one number contains another,—and, by which we divide one given number into as many equal parts, as there are units in another given number. Questions to be answered Orally. (1) How many kinds of operations are practised on numbers? (2) What are they called? (3) What is Addition? (4) What is Subtraction? (5) What is Multiplication? (6) What is Division? (7) Propose a question that you would solve by addition. (8) Propose a question that you would solve by subtraction. (9) Propose a question that you would solve by multiplication. (10) Propose a question that you would solve by division. (11) How can a question in multiplication be solved by addition? (12) How can a question in division be solved by subtraction? SECTION 5. MISCELLANEOUS EXAMPLES. 1. The population of the world has been estimated to be as follows. North America, twenty-six millions; South America, twelve millions; Europe, two hundred and twenty millions; Asia, five hundred millions; Africa, thirty-eight millions; Australia, four millions. What is the whole number? 2. In 1830, the national debt of the United States was 48 565 406 dollars; in 1831 it was 39 123 191 dollars. How much was paid in one year? 3. The national debt of England cannot be less than 1 900 000 000 dollars. How many years would it take to pay this debt, allowing ten millions of dollars to be paid annually? 4. What would be the expense of laying a rail-way from Louisiana to Maine; the distance being 1800 miles, and the rail-way costing 14 000 dollars a mile? 5. In how many days could a passage be effected from Maine to Louisiana, on the proposed rail-way; allowing a car to run 25 miles an hour, day and night? 6. How many days would it take a man to ride on horseback from Maine to Louisiana, riding 5 miles an hour, and 10 hours a day? 7. Light passes from the sun to the earth-a distance of 95 millions of miles-in about 8 minutes. What distance does light move in a minute? 8. The diameter of the earth is 7912 miles; and the diameter of the sun is 112 times as great. What is the diameter of the sun? 9. The income of the Bishop of Durham, in England, is 106 560 dollars per annum. How many clergymen would this support, on a salary of 800 dollars per annum? 10. Five men and three boys found a sum of money, and divided it so that each man had 43 dollars and each boy 26 dollars. What sum did they find? 11. If a trader buy 558 barrels of flour at 5 dollars a barrel, and pay 14 dollars for storage, for how much must he sell the flour, to gain 160 dollars? 12. Suppose 5 bushels of wheat to make a barrel of flour, how many barrels of flour can be made from 12 bins of wheat, each bin containing 95 bushels? 13. In 12 times 95, how many times 5? 14. If a farmer sell 45 acres of land at 38 dollars an acre, and divide the money equally among 4 sons and 1 daughter, what is each one's share? 15. A man, who owned 520 acres of land, purchased 376 acres more, and then divided the whole into 8 equal farms. How many acres did each farm contain? 16. In 520 plus 376, how many times 8? 17. If a man's income be 1349 dollars a year, and his expenses 3 dollars a day, how much will he lay up in a year; there being 365 days in a year? 18. A merchant gave 39 240 dollars for a cargo of sugar, and after selling it, found he had gained 1671 dollars. For how much did he sell it? 19. A merchant gave 18 dollars a hogshead for 245 hogsheads of molasses, and then sold the whole for 4000 dollars: did he gain or lose; and how much? 20. A lot of land was divided into 8 farms, and each farm contained 150 acres. How many acres were there In the whole lot? 21. If a man's expenses are 2 dol. a day, and his income 17 dol. a week; what will he save in 7 weeks? L 22. Three men bought a ship: the first man paid 2274 dollars; the second paid 3 times as much as the first, and the third paid as much as the first and second both. What was the price of the ship? 23. A hogshead holds 63 gallons. How many gallons of wine are there in 20 hogsheads; allowing that each hogshead wants 5 gallons of being full? 24. If a man earn 36 dollars a month, how many months will it take him to earn 576 dollars? 25. If a man earn 40 dollars a month, and spend 13 dollars a month, how many months will it take him to lay up 297 dollars? !! 26. A farmer having 20 barrels of pork, sold 9 barrels at 22 dollars a barrel, and the remainder at 19 dollars a barrel. What did he get for the whole? 407 27. If a trader, who has 152 barrels of flour, should lay out 1370 dollars in buying more flour, at 5 dollars a barrel, how many barrels would he have? 426 28. A trader hired 650 dollars, and in 6 months paid all but 92 dollars. How much did he pay? 29. What is the value of 139 yards of broad-cloth, at 7 dollars per yard? By the method of reasoning heretofore practised, we should say in this solution, 139 yards are worth 139 times 7 dollars; and thus we should make 7 the multiplicand, and 139 the multiplier. But since it is more convenient to make the smaller number the multiplier, we reason thus,-If the value of 1 yard were 1 dollar, the value of 139 yards would be 139 dollars; since the value of 1 yard is 7 dollars, the value of 139 yards is 7 times 139 dollars: and accordingly we make 139 the multiplicand, and 7 the multiplier. How 30. A trader bought 240 sheep, at 4 dollars a head, and paid for them in cows, at 20 dollars a head. many cows did he give? 31. If I pay 6 dollars an acre for the ploughing of 18 acres of land, and 100 dollars for having the whole planted and hoed, what does the cultivation cost? 32. How many cows at 19 dollars a head, will pay for 38 sheep at 4 dollars a head? 33. A farmer bougnt a field, valued at 150 dols., for which he gave 9 cows, valued at 11 dols. apiece, and the rest in money. How much money did he pay? 34. What number must be added to 9 times 14, ic order that the sum shall be 150? 35. If a stage travel 13 miles in the same time that a wagon travels 5 miles, how many miles will a stage travel while the wagon is travelling 65 miles? 36. Suppose that 9 bushels of wheat will fill a hogshead; how many hogsheads can be filled from a heap containing 149 bushels; and how many bushels will be left in the heap? 37. Charles and Joseph are studying arithmetic. Charles is 322 examples in advance of Joseph, but Joseph performs 55 examples in a day, and Charles, 41. In how many days will J. overtake C.? 38. Two men started together and travelled on the same road, at the rate of 7 miles an hour: but one of them rested 1 hour in every 3 hours, and the other rested 1 hour in every 4 hours. How far apart were they, at the end of 12 hours? 39. A drover, having 599 dollars, wishes to buy all the oxen he can pay for, at 34 dollars a head, and then lay out the remainder of his money for sheep, at 3 dollars a head. How many of each must he buy? 40. A, B, and C made up a purse of 500 dollars. A put in 16 dollars, and B put in 3 times as much. How much did C put in? 41. A merchant bought 64 tons of hemp at 215 dol lars a ton. How many ten-dollar bank notes did it take to pay for the hemp? 42. A merchant paid 9600 dollars for 43 tons of hemp. At how much must he sell the hemp per ton, in order to gain 247 dollars? 43. What number must be subtracted from 7342, in order that the remainder shall be 456? 44. What number must be multiplied by 30, in order that the product shall be 2130? 45. What number must be divided bv 15, in order that the quotient shall be 640? |