change 1554 ft. boards at $18.50 a thousand: which is in debt to the other, and how much? Ans. The lumber-merchant owes the coal-dealer $10.926. 13. A contractor furnished the following materials for a house: He paid for labor and additional material $742.50: how much did he make if he charged $1800 for building the house? Ans. $519.475. 14. A coal-dealer sold to a farmer at three separate times coal as follows: 4235 pounds, 4285 pounds, 4080 pounds, at $5.80 a ton; he agreed to take potatoes at 63 cents a bushel: how many bushels of potatoes does he get? Ans. 58. CHAPTER VII. DENOMINATE NUMBERS. SECTION I. DEFINITIONS. 88. A Denominate Number is one whose unit is named; as, 3 inches, 7 pounds, etc. 89. Numbers are of the same denomination when they have the same unit; as, 6 feet, 8 feet, etc. 90. A Compound Number is one consisting of several denominate numbers, but of the same species or measure; as, 6 yards, 2 feet, 3 inches. 91. A Measure is a unit used in estimating quantity. 92. A Quantity is measured by finding how often it contains the unit of measurement. 93. The principal measures are those of Value, Extension, Weight, Time and Angles. SECTION II. TABLES AND MEASURES. UNITED STATES CURRENCY. The currency of the United States was established by act of Congress in 1792. The unit of United States currency is the dollar. The currency of Canada is reckoned by the same scale as United States money, in dollars and cents. The unit of English currency is the pound sterling, indicated by the symbol £. The coin representing the pound sterling is called a sovereign. Its value in U. S. money is $4.8665. ORAL EXERCISE. 1. How many farthings in 6 d.? 8 d.? 12 d.? 2. How many pence in 3 s.? 4 s.? 10 s.? 8 far.? 12 far.? 3. How many shillings in 6 £? 5 £? 30£? 4. How many shillings in 48 d.? 480 far.? 16 £? 3 £ 6 s.? 5. How many pence in 3 £? 2 £ 3 s.? 1 £ 6 s. 6 d.? 6. How many £ in 40 s.? 960 d. ? WRITTEN PROBLEMS. 1. Reduce 6 £ 15 s. to shillings. SOLUTION. 6 £ 15 s. 20 120 15 135 s. Explanation.-1 £ = 20 s.; 6 £ = 6 × 20 s. = 120 s.; 120 s. +15 s. = 135 s. Hence, 6 £ 15 s. = 135 s. 2. Reduce 1820 d. to pounds. SOLUTION. 12)1820 d. Explanation. In 1820 d. there are as many shillings as 12 is contained times in 1820, or 151 s. and 8 d.; in 151 s. there are as many pounds as 20 is contained times in 151, or 7 £ 11 s. =7£ 11 s. 8 d. 4. Reduce 18 £ 10 s. 5 d. to pence. 5. Reduce 1872 d. to £, s. and d. 6. Reduce 16842 far. to £, s., d. and far. Hence, 1820 d. Ans. 332 s. Ans. 4445 d. Ans. 7 £ 16 s. Ans. 17 £ 10 s. 10 d. 2 far. WEIGHT. 94. Weight is the quantity of matter in bodies as estimated by the force with which they are attracted to the earth's centre. AVOIRDUPOIS WEIGHT. 95. Avoirdupois Weight is that used in weighing produce, coal, iron, groceries, etc. 1 lb. avoirdupois equals 7000 grains. In collecting duties at the U. S. custom-houses, and in freighting and selling coal at wholesale, what is called the long ton (2240 lb.) is used. In this ton 1 qr. equals 28 lbs.; and 1 cwt. equals 112 lb. The following units are also used: ORAL EXERCISE. 1. How many ounces in 6 lb. avoirdupois? 12 lb.? 10 lb.? 2. How many pounds in 2000 oz.? 2400 oz.? 3. How many pounds in 3 T.? 4. How many pounds in 9 qr.? 6 T. 3 cwt.? 3 cwt. 3 qr. 5. A farmer exchanged 1 T. 3 cwt. of hay at 80 cts. per cwt. for delaine at 40 cts. a yard: how many yards did he get? Ans. 7 T. 6 cwt. 2 qr. 15 lb. 10 oz. 5. What is the value of 2 lb. 4 oz. of butter at 30 cents a pound? Ans. 67 cents. 6. What is the value of 3 lb. 5 oz. of cheese at 22 cts. a pound? Ans. 7214 cents. 7. What will 5 barrels of beef cost at 5 cts. a pound? Ans. $55. 8. What will 19 barrels of flour cost at 3 cts. a pound? Ans. $130.34. 9. What is the value of 16840 lb. of wheat at $1.20 a bushel ? Ans. $336.80. 10. A farmer sold 64 bags of wheat, each weighing 1834 lb., at $1.30 per bushel: how much did he get for his wheat? Ans. $254.451. TROY WEIGHT. 96. Troy Weight is used in weighing gold, silver, gems and jewels. |