Explanation. Observe the rule in Fractions, lesson 70, and the two preceding rules for multiplying and dividing compound numbers. 2. A man gave $82 for 1 chal. 7 bu. 3 pks. of Sidney coal; how much could he have obtained for $1, at the same rate? Ans. 5 bu. Explanation. Observe the rule in Fractions, lesson 73, and the two preceding rules for multiplying and dividing compound numbers. 3. Multiply 6 lbs. 2 oz. 10 grs. by . 4. Multiply 103 23 by 41. Ans. 9 oz. 5 pwts. 14 gr. Ans. 3lb 83 33 19. 5. Divide 10 sq. rods 2.25 sq. ft. by .6. Ans. 16 sq. rods 185.25 sq. ft. 6. If you buy 4 C. 9 ft. of wood for $243, how much can you buy for $1, at the same rate? Ans. 1 ft. 105 cubic ft., or 1 ft. 10 cubic ft., about. 7. A trader sold of a bin of wheat for $12.50; the bin, on measurement, was found to contain 18 bu. 3 pks.; how much did he sell for $12.50, and how much for $1 ? Ans. 7 bu. 3 pks. 2 qts. for $ 12.50, and 2 pks. 4 qts. for $1. 8. How much is 4 times 2 hhds. 1 bl. 7 gals. of wine? Ans. 12 hhds. 25.375 gals. 9. A laborer being 8 h. 45 min. doing a piece of work, another man agreed to perform a similar job in & of the time; how long was that? Ans. 7 h. 17 min. 30 sec. 10. A portion of the circumference of a circle, containing 11° 34′ 06′′, is to be divided into 54 equal parts; how large will each portion be? Ans. 2° 06′ 12′′. PROMISCUOUS QUESTIONS IN FEDERAL MONEY AND COMPOUND NUMBERS. LESSON 117. To be performed in the mind. 1. A piece of land is divided into two house lots, one of which is 25 ft. 8 in. wide, and the other 30 ft. 6 in. wide; what is the width of the whole piece? 2. If the piece had been divided into two lots of equal widths, how wide would each have been? 3. If I buy 3 C. 6 ft. of pine wood for $10, how much do I get for $1? What do I give a foot for it? 4. A trader had 16 gals. 2 qts. of vinegar in a cask; how much was there left after selling 3 qts. ? 1 gal. 2 qts. ? 3 gals. 3 qts. ? 5. A girl in Boston bought a silver pencil case for 75 cents, a sheet of drawing paper for 1 shilling, and four quills for ninepence; she gave a 2-dollar bill in payment; what sum did she receive back? 6. What quantity of silver is there in 4 silver pitchers, each of which weighs 1 lb. 5 oz. ? 7. A man in Albany paid 3 shillings and sixpence for a cane, and $34 for an umbrella; what sum did he give for both? 8. How many square yards are there in a piece of ground 15 ft. square? of a ton 9. What must I give for 16 yds. of cloth at $ 21 a yard? 10. How many hundred weight are there in of anthracite coal? How many pounds? 11. How will you contrive to pay a man 70 cents, in Pittsburg, if you have in your purse, of a dollar, of a dollar, 2 levies, 3 fips, and 4 cents? How near can you pay him the exact sum ? 12. A man bought of a load of hay containing 1 T. 4 cwt.; what quantity did he obtain ? LESSON 118. For the Slate. 1. A man paid $.90 for of a quantity of hay, estimated to be 2 T.; what price a hundred weight did he give? Ans. $.561. 2. If a boatman in New York charge you 6 shillings for rowing you over the Hudson River and back again, how many cents must you pay him? Ans. 75 cts. 3. A man owns one farm containing 115 A. 2 qrs. 13 sq. rods; another containing 37 A. 30 sq. rods, and a third containing 18 A. 3 qrs. ; how much land has he? Ans. 171 A. 2 qrs. 3 sq. rods. 4. A trader sold 2 bu. 1 pk. of beans for $5.94; what price did he get a peck? Ans. $.66. 5. If you retail 1 quintal of cod fish at 4 cents a pound, 2 bls. of beef at 10 cents a pound, and 1 bl. of flour at 33 cents a pound, what sum will you get for the whole ? Ans. $51.83. 6. What part of a pint, wine measure, is Toog of a hogshead? Ans. 7. A young man is 19 years 86 days old, and his sister 17 years 119 days old; what is the difference of their ages? Ans. 1 yr. 332 d. 8. A man boarded in Northampton, Massachusetts, 12 weeks, at 15 shillings a week; what sum in Federal money must he pay his landlord? Ans. $30. 9. A man sold 1 A. 2 qrs. 8 sq. rods of land at 8 cents a square foot; what sum did it bring him ? Ans. $5,401.44. 10. What part of a cord of wood, in common fractions, are 48 cubic ft. ? LESSON 119. Ans.. 1. The distance between two headlands on the coast of Maine, was measured, and found to be 6,530 fathoms ; what is this distance expressed in miles and rods ? IT Ans. 7 m. 134 rods. 2. If a man pump 27 gals. 3 qts. 1 pt. of water in 1 minute, how much can he pump in 9 h. 4 min. 30 sec. ? Ans. 15,177 gals. 3 qts. 1 pt. 2 gi. 8 15 3. What must I pay for 2 T. 7 cwt. 3 qrs. of hay, at the rate of $17 a ton? Ans. $40.582. 4. How many square feet are there in a garden 5 rods 12 ft. 6 in. long, and 2 rods 8 ft. wide? Ans. 3,895 sq. ft. 5. How many hours and minutes are there in of a day? Ans. 12 h. 48 min. 6. 6 silver tea spoons weigh 2 oz. 9 pwts. 12 grs. ; what is the weight of each? Ans. 8 pwts. 6 grs. 7. 2 T. 3 cwt. 2 qrs. of American bar iron was sold for $130.50; what price a ton did it bring? Ans. $60. 8. How many pieces of iron, each weighing 1 lb. 4 oz., can be cut off from a bar weighing 2 cwt. 1 qr. 8 lbs. ? Ans. 208 pieces. 9. If you sell 3 tubs of butter, each of which weighs 56 lbs. 13 oz. what is the whole quantity disposed of? Ans. 198 lbs. 131 oz. 10. There is a block of wood 4 ft. long, and 2 ft. 6 in. high, containing 12.5 cubic ft.; how wide is it? Explanation. See Division, lesson 51. Ans. 1 ft. 3 in. PERCENTAGE. LESSON 120. Per cent. is a contraction of the Latin per centum, and signifies per hundred. 1 per cent. of any number is T of it, or .01 of it; 2 per cent. is .02 of it, 3 per cent. is .03 of it, 25 per cent. is .25 of it, 120 per cent. is 1.20 of it, and 100 per cent. of any number is just equal to it, &c. Also, per cent., or of 1 per cent. of any number, is of .01, or .005 of it; per cent. is .0025 of it, and 21 per cent. is .025 of it, &c. Any per cent. of a number, then, is so many hundredths of that number. Write on your slate answers to the following questions. 6 per cent. of any number? What is per cent. of any number? What is 100 per cent. of any number? What is per cent. a contraction of, and what does it signify? What is 1 per cent. of any number? 2 per cent.? 3 per cent.? 25 per cent.? 120 per cent.? 100 per cent.? per cent.? per cent.? 2 per cent.? What is any per cent. of a number? What per cent. of any number, that is, how many hun The number of which we are to get a certain per cent. is called the principal, and the per cent., considered as hundredths, is called the rate. LESSON 121. 1. A trader intrusted a man with $225, 4 per cent. of which he was directed to invest in books, and the rest in West India goods; what sum must he lay out in books? OPERATION. $225 .0 4 $9.00 Ans. 2. A man let a house in Baltimore for a rent of $950 a year, with a condition that 8 per cent. of the rent should be expended in repairs on the house; how many dollars a year must be laid out in repairs? Ans. $80.75. 3. A merchant having $2,507.75 in a bank, drew out 20 per cent. of it; how much was that? Ans. $501,55. 4. What is 435 per cent. of $ 1,000? 5. A merchant had 3 bales of cotton, the first of which contained 4 cwt. 1 qr. 27 lbs., the second 5 cwt. 7 lbs., and the third 3 cwt. 3 qrs. 8 lbs.; they were so much damaged during a fire that 18 per cent. of the cotton was destroyed; what quantity was that? Ans. 2 cwt. 1 qr. 17 lbs. 10.24 oz. What is called the principal? The rate? |