16. If a link contains 7.92 inches, how many inches are there in 75 links? Ans. 594. 17. A farmer exchanged 28 bushels of wheat at $1.25 a bushel for 200 pounds of sugar at 134 cents a pound, and the balance in cash: how much is due him? Ans. $7.50. SECTION VI. DIVISION OF DECIMALS. WRITTEN PROBLEMS. 1. Divide 578.5728 by 8.32. SOLUTION. Ans. 69.54. Explanation.-578.5728 is equal to 5785728; 8.32 8.32)578.5728(69.54 equals 3; 5785738 divided by 13=954, 4992 7937 7488 4492 4160 69.54. 10000 1009 or NOTE. Since the quotient multiplied by the divisor equals the dividend, it is evident, according to the preceding Section, that the number of decimal places in the divisor, plus the number in the quotient, equals the number in the dividend; hence, the number in the dividend, less the number in the divisor, equals the number in the quotient. 3328 From the foregoing solution and explanation we derive the following rule for division of decimals. RULE. Divide as in simple numbers, and point off as many decimal places in the quotient as the number of decimal places in the dividend exceeds the number of those in the divisor. NOTE. If the number of decimal places in the divisor exceeds the number in the dividend, first annex enough ciphers to the dividend to make the number of places equal to the number in the divisor. To find the Cost when the Price of 100 or 1000 and the Quantity are given. WRITTEN PROBLEMS. 1. What cost 340 cabbages at $4.20 a hundred? Ans. $14.28. 2. What will 675 ft. of boards cost at $18.50 per thousand? From the above processes and explanations we derive the rules to find the cost of articles sold by the hundred or thousand. RULES. 1. Multiply the cost per hundred by the total quantity, and cut off two places from the right hand. 2. Multiply the cost per thousand by the total quantity, and cut off three places from the right hand. 3. Find the value of 17745 bricks at $7.50 per thousand. Ans. $133.0875. 4. What cost 23425 feet of hemlock lumber at $15 a thousand? Ans. $351.375. 5. A lumber-merchant sold 60000 lath at 30 cents a hundred, and 1250 feet of boards at $21.50 a thousand: how much did he get for both? Ans. $206.875. 6. A grocer bought 320 cucumbers at 40 cents a hundred, and 115 cabbages at $3.50 a hundred: what did he pay for both? Ans. $5.305. 7. What is the cost of 15520 bricks at $7 a thousand, and 5760 at $12.50 a thousand? Ans. $180.64. 8. A lumber-merchant sold the following bill: 2500 ft. boards at $27.50 per at $24 per M; M; 1650 laths at 32 cts. per hundred; 1520 pickets at $15 per M; 7500 shingles at $6.50 per M. What did he receive for the whole amount of lumber sold? CASE II. Ans. $190.58. To find the Cost when the Price of a Ton and the Number of Pounds are given. WRITTEN PROBLEMS. 1. At $12 a ton what will 2315 pounds of hay cost? From these solutions we derive the following RULES. 1. Multiply the cost of a ton by the number of pounds, and divide by 2000. 2. Multiply one-half the cost of a ton by the number of pounds, and divide by 1000. 2. What will 1875 pounds of coal cost at $6 a ton? Ans. $5.621. 3. What is the cost of 6340 pounds of coal at $5.75 a ton? Ans. $18.2275. 4. What must I pay for 7850 pounds of stone at $2.20 a ton? Ans. $8.635. 5. A farmer bought 3350 pounds of plaster at $5.20 a ton: how much did it cost? Ans. $8.71. 6. When pig iron is worth $32 a ton, what is the value of a car-load containing 15640 pounds? Ans. $250.24. 7. A farmer sold 2520 pounds of hay at $22 a ton, and 1860 pounds of straw at $16.50 a ton: how much did he get for both? Ans. $43.065. 8. If silver ore is worth $190 a ton, what is the value of 10870 pounds? Ans. $1032.65. 9. A dealer sells 130 sacks of salt, each containing 230 pounds, at $25 a ton: how much does he get? Ans. $373.75. 10. A coal and lumber dealer sold the following: 18640 pounds nut coal at $4.25 per ton; 6350 stove coal at $5 per ton ; 1865 feet flooring-boards at $25 per M; 12000 lath at 45 cents a hundred. What was the amount of the bill? SECTION VIII. Ans. $156.11. PROMISCUOUS PROBLEMS IN DECIMALS. 1. A farmer had 3 fields, containing as follows: 16.475 acres, 12.227 acres and 18.605 acres: how many acres in the three fields? Ans. 47.307. 2. John walks 3.745 miles, and James 3.8005 miles: which walks the farthest, and how much? Ans. James-.0555 miles. 3. A merchant owned 64.803 acres of land; he bought 10.7045 acres, and sold all but 16.455 acres: how many acres did he sell? Ans. 59.0525. 4. What is the value of 7.5 tons of hay at $18.75 a ton? Ans. $140.625. 5. A farmer exchanged 12.55 tons of hay at $17.75 per ton for 20 head of cattle at $16.25 a head, the balance to be paid in cash: how much cash did he have to pay? Ans. $102.2375. 6. If a wine-merchant sell 27.5 casks of wine, each containing 31.25 gallons, from a stock of 1000 gallons, how much remains? Ans. 140.625 gallons. 7. A merchant purchased oil at $9.43 per barrel, and sold it at $11.48 a barrel, and gained $451: how many barrels did he have? Ans. 220 barrels. 8. A store was valued at $9000; it was insured for .625 of its value what is that man's share of the insurance who owns Ans. $2531.25. .45 of the stock? 9. A store worth $8800 was damaged by fire, but of its goods were saved; A owns .40; B, .35; and C, the remainder of the stock: what was the value of each one's share of the goods saved? Ans. A, $2112; B, $1848; C, $1320. 10. A bricklayer furnished 17840 bricks at $7.50 a thousand, and worked 43 days at $2.75 a day: what is his bill? Ans. $252.05. 11. A gardener paid as follows: for ploughing, $26.50; for seed, $2.375; for labor, $40.625; for cultivating, $12.50; and for hauling and marketing, $26.25. He sold 850 heads of cabbage at $5.25 a hundred, 1275 cucumbers at $.75 a hundred, 840 ears of corn at 15 cts. a dozen, and 325 bushels of potatoes at $1.75 a bushel. What was his profit for the year? Ans. $525.1875. 12. A coal-merchant sold to a lumberman 5 loads of coal, as follows: 2840 pounds, 2725 pounds, 2742 pounds, 2930 pounds, 2563 pounds—all at $5.75 a ton; and bought in ex |