18s.= 1£2s., 7 times 18s. must equal 7£ 14s., or 6£, 68., to which adding 4s., (from the previous product,) we have 6£, 10s., as before. 16. What is the product of 37£, 14s. 2d. 3qr. multiplied by 9? by 6? 17. What is the product of 23 lb. 4 oz. 16 dwt. 22 gr. multiplied by 8? by 4? 18. What is the product of 13 cwt. 2 qr. 17 lb. 13 oz. 9 dr. multiplied by 6? by 5? 19. What is the product of 6 T. 18 cwt. 1 qr. 26 lb. 2 oz. 1 dr. multiplied by 7? by 9? 20. What is the product of 9 bu. 3 pk. 7 qt. multiplied by 9? by 3? 21. What is the product of 4 rd. 3 yd. 2 ft. 8 in. multiplied by 8? by 6? 22. What is the product of 9 gal. 2 qt. 1 pt. multiplied by 5? by 2? 23. *What is the product of 1 m. 4 fur. 39 rd. 5 yd. 1 ft. 3 in. multiplied by 9? by 4? 24. What is the product of 8 w. 1 d. 23 h. 59 m. 56 sec. multiplied by 7? by 5? 25. What will .03 of a box of raisins cost at $2.375 per box? Explanation. Since 1 box costs $2.375, .03 of a box will cost .03 of $2.375. .01 of $2.375, found by removing the decimal point two places toward the left, is $.02375, and .03 must, therefore, be 3 times $.02375. The following form of writing the work exhibits clearly the change in the position of the point and the reason for it, and should be carefully followed by the pupil in all similar examples, till much practice has made him perfect in them : $2.375 .01 of $2.375 = $.02375 3 times $.02375 $.07125 cost of 1 box. cost of .01 of a box. 26. What will .9 of a yard of broadcloth cost at $3.25 per yd.? 27. If a bushel of tomatoes weigh 48.37 lb., what will .3 of a bushel weigh? *In performing this example much labor may be saved by observing that the multiplicand is only 3 in. less than 1 m. 5 fur. Similar things can frequently be taken advantage of. 28. If a train of cars moves at the rate of 27.29 miles per hour, how far will it move in .07 of an hour? 29. If a cubic yard of distilled water weighs 1677.5 lb., how much does .09 of a cubic yard weigh? 30. If pine weighs .8 as much as an equal bulk of water, what will a cubic foot of pine weigh, a cubic foot of water weighing 62.5 lb. ? 31. What will .4 of a ton of iron cost at $47.93 per ton? 32. What will .8 of a bag of coffee cost at $13.93 per bag? 33. What will .7 of a ton of coal cost at $5.875 per ton? 34. If Mr. Smith uses 9.678 tons of coal per year, and Mr. Parkhurst uses .7 as much, how many tons does Mr. Parkhurst use ? NOTE. The term per cent is often used in arithmetic, and in business transactions, instead of one-hundredths. Thus, 6 per cent has the same meaning as 6 one-hundredths. 8 per cent .08 = 180. 5 per cent of 340 acres = .05 of 340 acres. 6 per cent of $86.38.06 of $86.38. Every number is 100 per cent of itself. 35. A teamster carted 7486 bushels of potatoes to a rail-road depot, receiving in payment 9 per cent of them. How many bushels did he receive? 36. A man who owned 378.37 acres of land gave 8 per cent of it to his son. How many acres did he give to his son? 37. A city merchant agrees to sell for a country farmer whatever produce the latter may send to him, on condition that he shall receive for his trouble 5 per cent of the money he receives for the produce. Under this arrangement he sells produce to the value of $1768.37. What ought he to receive for his trouble? NOTE. A merchant who makes it his business to buy and sell goods for others, is called a Commission Merchant. The money he receives for his services is called his Commission. For instance: - In the last example the merchant receives a commission of 5 per cent on the value of the produce he sells. He will deduct this commission from the amount of the sales before paying the farmer. 38. A commission merchant sold cloth for a manufacturer, to the amount of $7643.79, receiving a commission of 3 per cent. What did his commission amount to? How much money ought he to pay the manufacturer ? 39. A commission merchant buys goods for me to the amount of $387.46, for which he charges a commission of 2 per cent. What will his commission amount to? How much money must I send him to pay for the goods and commission? 40. Mr. Moore borrowed some money of Mr. Boyden, agreeing to pay him, for each year's use of it, a sum equal to 6 per cent of the money he had borrowed. He borrowed $125.63, and kept it just one year. How much ought he to pay for the use of it? How much, then, ought he to pay Mr. Boyden in all? NOTE. Money paid, as in the above example, for the use of money is called Interest. The money used is called the Principal. Interest is usually reckoned at a certain per cent of the principal for each year that it is used. The percentage paid for each year is called the Rate Percent. The interest and principal added together form the amount. 41. What is the interest of $137.84 for 1 year at 6 per cent? 42. What is the interest of $487.31 for 6 months at 6 per cent per year? Suggestion. Since the rate for 1 year is 6 per cent, the rate for 6 months must be of 6 per cent, which is 3 per cent. The interest for 6 months will, therefore, be 3 per cent of the principal. 43. Mr. Adams borrowed of Mr. Wales $718.63, for which he agreed to pay interest at 6 per cent. At the end of 6 months he paid the principal and interest. How much did he pay? 44. What is the interest of $47.83 for 4 months at 6 per cent? 45. What will 49.67 barrels of apples cost at $3 per barrel? Solution. If one barrel costs 3 dollars, 49.67 barrels will cost 49.67 times 3 dollars, which is equivalent to 3 times 49.67 dollars. The work would be written thus Another Solution. It is evident that if each barrel should cost a dollar, all would cost as many dollars as there are barrels bought, which in this instance would be $49.67. But if, at $1 per bbl., they cost $49.67, at $3 per bbl. they would cost 3 times $49.67. The work may be written thus 49.67 bbl. at $3 per bbl. $49.67 cost at $1 per bbl. 3 times $49.67= $149.01 =cost at $3 per bbl. —Ans. NOTE. The second of the above forms exhibits more clearly than the first the change in the denomination of the 49.67, and is particularly well adapted to exhibit the changes when there are decimal fractions in multiplier and multiplicand, as the following example may show. 46. What will 43.75 pt. of beans weigh, if 1 pt. weighs .9 of a pound? NOTE. It will in the end be a saving of labor for the pupil to write out his work for a time as fully as the work of the last two examples is written. 47. Mr. Rice has a basket which holds .7 of a bushel, and he has peaches enough to fill it 26.43 times. How many bushels of peaches has he? 48. If a man walks .06 of a mile per minute, how many miles will he walk in 87.29 minutes? 49. What will 37.49 lb. of saleratus cost at $.08 per lb.? 50. What will 178.69 bbl. of flour cost at $7 per bbl. ? 51. What will 27.96 firkins of butter cost at $9 per firkin? 52. What will be the weight of 3794 cannon balls, each ball weighing 8 lb. ? 53. If a soldier eats 4 lb. of meat in a week, how many pounds will 2896 soldiers eat-in the same time? 54. If a paper of pins costs $.07, how much will 4978 papers cost? 55. If 1 pint of oats weighs .6 of a lb. and yields .4 of a lb. of oat-meal, how many pounds will 67.98 pints of oats weigh? How many pounds of oat-meal will they yield? 56. If a bushel of potatoes is worth $.5, how much are 133.75 bushels worth? 57. What will .3 of a cwt. of coffee cost at $14.83 per cwt.? 58. What will 14.83 lb. of tea cost at $.3 per lb. ? 59. What will 8 boxes of lemons cost at $3.187 per box? 60. What will 3.187 cwt. of sugar cost at $8 per cwt.? 61. 8734 yd. how many feet? 62. 6743 weeks how many days? 64. 576.37 sq. yd = how many square feet? In such examples as the above there is no need of writing the multipliers, as they may be known from the table of the weight or measure used. In reducing to any denomination of which there are units already expressed, it will usually be more convenient to add those units at the time we make the reduction. Method of writing the work of the last example: The following abbreviated method of writing the work may be adopted after the above is perfectly familiar: 70. 9, 113,6 3, 29 = how many scruples? 71. 8, 33, 73, 19 how many scruples? 72. 937 le. 1 m. 5 fur.= how many furlongs? 73. 286 le. 2 m. 7 fur. how many furlongs? 74. What will 37 bu. 2 pk. 3 qt. 1 pt. of cherries cost at 4 cents per pint? 75. What will 114 bu. 3 pk. 2 qt. of wheat cost at 1 cent per gill? 76. What will 17 gal. 3 qt. 1 pt. 3 gi. of oil cost at 5 cents per gill? 77. What will 93 gal. 2 qt. 1 pt. 2 gi. of brandy cost at 8 cents per gill? F. It often happens that a number used as a multiplier is the product of two or more factors. In such cases it is some |