166. MISCELLANEOUS PROBLEMS. 1. What cost 43.45 acres of land, at $38.5 an acre ? Ans. $1672.825. 2. What cost 57.75 tons of hay, at $12.25 a ton? Ans. $707.4375. 3. There are 16.5 feet in a rod; how many feet in 246.15 rods? Ans. 4061.475. 4. A man sold 35.25 pounds of butter for $5.875; how much is that a pound? Ans. $0.166+. 5. 31.25 yards of muslin cost $7.8125; how much is that yard? Ans. $0.25. 6. There are 31.5 gallons in a barrel; how many barrels in 2756.25 gallons? Ans. 87.5 barrels. 7. If 25.5 yards of cloth cost $195.375; how much will 45.25 yards cost? Ans. $346.696+. 8. There are 7.92 inches in a link; how many inches in 990 links? Ans. 7840.8 inches. 9. If an imperial gallon contains 277.274 cubic inches, how many cubic inches in 328.55 gallons? Ans. 91098.3727. 10. A bought 78.25 acres of land at $128.5 an acre, and sold it for $9781.25; what was the loss per acre? Ans. $3.50. 11. A gallon of distilled water weighs 8.33888 pounds; how many gallons in 10000 pounds of such water? Ans. 119.92+. 12. A drew 41.25 barrels, of 31.5 gallons each, from a cistern containing 2000 gallons; how much remained? Ans. 700.625 gallons. 13. Bought 3 loads of wood, the first containing 1.02 cords, the second 1.05 cords, and the third .945 cords; what did it cost at $3.60 a cord? Ans. $10.854. 14. A cubic inch of water weighs 252.458 grains avoirdupois ; how many cu. in. in 157786.25 grains? Ans. 625 cu. in. 15. A man having $8000, left of it to his wife, to his daughter, and the rest to his son; what did each receive? Ans. Son, $3333.331. 16. B bought 45 hundred weight of iron, at $7.25 a cwt., of which he paid in sugar, at $8.25 a cwt., and the remainder in cash; how much money was paid? Ans. $65.25. 17. A and B own 4320 acres of land, which they divide in the proportion of .45 and .75; what did each receive? SUG. 45 is to .75 as 45 to 75, etc. Ans. 1620; 2700. 18. A and B bought 859.25 bushels of potatoes, and .50 of A's equals .75 of B's; how many bushels belong to each? 343 Ans. 515.55; 343.70. · 19. Divide the number 76.25 into two parts which are to each other as .25 to .75. Ans. 19.0625; 57.1875. 20. A man paid $1000 for land, giving $76.25 an acre for 27.25 acres, and $85.75 for the remainder; how many acres did he buy? Ans. 49.661 acres. 21. A man bought 345.75 tons of hay, at $16.25 a ton, of which he sold at $17.75 a ton, and the rest at cost; how much was the gain? Ans. $172.874. 22. A bought a lot of wheat and sold .15 of it to one man, and..25 of it to another, and kept 572.85 bushels; how much did he buy? Ans. 954.75 bu. 23. A, B, and C bought 645 tons of hay, of which A takes, B, and C the remainder; how much did each receive? Ans. C, 134.375 tons. 24. A man gives .12 of his income to the poor, .25 to educational purposes, spends .45 for his living, and saves the remainder, which is $284.76; required his income. Ans. $1582. 25. If $836.80 be divided into two parts to each other as .25 to .45, it will respectively give A's and B's fortune; what are their fortunes? Ans. A's, $298.855; B's, $537.942. 26. How many cords of wood, at $5.121 a cord, must a man give for 91.25 bushels of wheat, at $1.40 a bushel, and 85 bushels of rye, at $1.25 a bushel? Ans. 45.66 cords. 27. A expended $6210 for grain, of it being for wheat, at $1.25 a bushel, of it for corn, at $0.75 a bushel, and the remainder, rye, at $1.12 a bushel; how many bushels of each kind did he purchase? Ans. Wheat, 1656 bu.; Corn, 2070 bu.; Rye, 2300. SECTION VI.' DENOMINATE NUMBERS. 167, A Denominate Number is a number in which the kind of unit is named. There are two classes; 1st, in which the unit is natural; 2d, in which it is artificial. Natural units are such as exist in nature; as, trees, stones, etc. Artificial units are those which are agreed upon to measure quantity of magnitude; as, foot, pound, etc. 168. A Compound Number is a number consisting of several denominate numbers of the same kind of quantity; as, 4ft. 6in. NOTE.-Nature regarded as how many and how much gives rise to two kinds of quantity, quantity of multitude and quantity of magnitude. Quantity of multitude is primarily expressed in numbers, and quantity of magnitude can only be clearly understood by a numerical expression also. Thus, even the how much is estimated by being conceived as the how many. MEASURES. 169. A Measure is that by which quantity is estimated numerically. Measures are of seven kinds : 4. Surface, or Area. 7. Angles, or Circular Measure. MEASURES OF VALUE. 170. Money is the measure of the value of things. of two kinds, coins and paper money. It is 171. Coin is metal prepared to circulate as money. The metals generally used are gold and silver. Paper Money consists of printed promises duly authorized to circulate as money, to pay the bearer a certain amount. NOTE TO THE TEACHER.-With quite elementary classes, it will be well to omit the notes upon the tables until the review. Upon review and with advanced classes, they will be found among the most interesting and instructive things in the book, UNITED STATES MONEY. 172. United States, or Federal Money, is the money NOTES.-I. Federal Money is founded upon the decimal system, the dollar being the unit. It was adopted in 1786. II. The word dollar is supposed to be derived from the German Dale, a town; or thal, a dale, or valley, in which they were first coined. Another theory derives it from the Anglo-Saxon dæl, a portion, it being a portion of a ducat; and another, from thaler, which is supposed to be from talent. III. The term dime is from the French disme, meaning ten; the term cent is from the Latin centum, for hundred; the term mill is from the Latin mille, a thousand. The cent was proposed by Robert Morris, and named by Thomas Jefferson. IV. There are several theories for the origin of the dollar mark: 1st. That it is a combination of U. S., the initials of United States. 2d. That it is a modification of the figure 8, the dollar being formerly called a piece of eight and designated by the symbol . 3d. That it is derived from a representation of the "Pillars of Hercules," consisting of two pillars connected with a scroll. The coins containing this were called "pillar dollars." 4th. That it is a combination of H. S., the mark of the Roman money unit. 5th. That it is a combination of P. and S., from the Spanish peso dura, signifying hard dollar. In Spanish accounts the S is written upon the P and placed after the sum. V. The coins are of gold, silver, and copper. The gold coins are the double eagle, eagle, half-eagle, quarter-eagle, three dollars, and one dollar. The silver coins are the half-dollar, quarter-dollar, dime, half-dime, and 3-cent piece. The gold and silver coin consist of 9 parts pure metal and 1 part alloy, except the 3-cent piece, which is alloy. The alloy of silver coin consists of pure copper, and of gold coin, of equal parts of silver and copper. The old cent was pure copper, the new cent consists of 88 parts copper and 12 parts nickel. The mill is not coined. 1 ENGLISH MONEY. 173. English, or Sterling Money, is the money of England. NOTES.-I. The term Sterling is supposed to be derived from Easterling, the name given to the early German traders who came from the east to England. II. The name farthing is a modification of "four things," the old English penny being marked with a cross so that it could be broken into two or four pieces, called half-penny and four things. III. The pound, as a measure of value, was derived from the pound as a measure of weight, 240 pence formerly weighing a pound. The guinea is so called because the gold of which it was first made came from Guinea in Africa. IV. The symbols £, s., d., q., are the initials of the Latin words libra, solidus, denarius, and quadrans, signifying, respectively, pound, shilling, penny, and quarter. V. The Pound Sterling is represented by a gold coin called a Sovereign. Its value in United States money is $4.84. How many 1. Farthings in 6 pence? 2. Pence in 8 shillings? 3. Shillings in 108 pence? 4. Shillings in 25 pounds? 5. Pounds in 480 shillings? 6. Pence in 124 guineas? Problems for written NOTE.-Problems similar to the above may be presented under each table. They are of course to be solved mentally. solutions will now be given. 1. How many pence in 16£ 11s. 10d.? SOLUTION. In one pound there are 20 shillings, and in 16£ there are 16 times 20 shillings, which increased by 11s. are 331 shillings. In one shilling there are 12 pence, and in 331 shillings there are 831 times 12 pence, which increased by 10 pence equals 8982 pence. OPERATION. 20 331 12 8982d. Ane. |