SECTION II. THE GOLDEN RULE, OR RULE OF THREE DIRECT. This Rule has three numbers given to find a fourth, which shall bear the same proportion to the third, as the second does to the first. Two of the given numbers in your ques. tion are always of the same name or kind, and the other is of the same name of the fourth, or number sought, which is the answer. The first number is often known by the word If, or At. The third is a demand, and is known by the words, What wil, What cost, How much, How far, &c. The first and third words are always placed before the first and third numbers, in the given question. Rule. Write the word If, or At, down first, and place your numbers to the right hand of If, or At, so that the first and third numbers will be of the same name or kind, and the second number of the same name as the answer. Bring the first and third numbers, or terms, to the least denomi. nation mentioned in either, and the second term or number to the least denomination in it. Then multiply the second and third numbers together, and divide that product by the first term or number, and the quotient will be the same Dame or denomination you left the second in, and is the answer to the question, which is the fourth term, or number sought, and may be reduced to a higher name, yet retaining the same value. Or, divide the second number by the first, and multiply the quotient by the third, and the product will be the answer. Or, divide the third number by the first, and multiply the quotient by the second, and the product will be the answer. Or, divide the first number by the third, and the second by that quotient, and the last quotient will be the answer. EXAMPLES. 1. If 8 cents be paid for a pound of sugar, how much must I pay for 112 lbs. at that rate? Ans. 8 dolls. 96 cts, 16. 16s. If 1 : 8 cts. 112 Ans. 896 cts. Or 8 dolls. 96 cts. 2. If 8 dolls. 96 cts. be paid for 112 lbs. of sugar, what is that a pound, at that rate? Ans. 8 cents. 3. If I paid 8 dollars 96 cents for 112 lbs. of sugar, what quantity can I get for 8 cents, at that rate: Ans. 1 lb. 4. How much corn can I get for 100 dollars, at the rate of 25 cents a bushel? Ans. 400 bushels. 5. Paid 100 dollars for 400 bushels of corn; what is that a bushel? Ans. 25 cents. 6. Bought 400 bush. of corn for 100 dolls. what quantity can I get, at that rate, for 2 dimes 5 cents ? Ans. 1 bushel. 7. If I work for 50 cents a day, how much is my wages at the end of 6 months, (deducting 26 days for Sundays) allowing the 6 months to be 183 days ? Ans. 78 dolls. 50 cts. 8. Paid 51 dolls. 6 cts. for a flock of sheep, at 1 dol. 11cts. a head; how many did I buy? Ans. 46. 9. Bought 3 hhds. of sugar, each weighing 8 cwt. 1 gr. 12 lbs. at the rate of 7 dollars 26 cents per cwt. What did I pay? Ans. 182 dolls. 1 ct. 8 m. 10. What will 4 cwt. 2 qrs. 8 lbs. of iron come to, at 48 cents for 4 pounds? Ans. 61 dolls. 44 cts. 11. What will 596 lbs. of pork come to, at 2 cts. a pound? Ans. 7 dolls. 92 cts. 12. If 20 bushels of oats last 4 horses 1 week, how many weeks will 100 bushels last them, at that rate? Ans. 5 weeks. 13. Bought a piece of cloth for 33 dolls. at 75 cts. a yard; how many yards were in the piece? Ans. 44 yards. 14. A merchant bought 14 pipes of wine, and is allowed six months credit, but for ready money, gets it 8 cents a gallon cheaper. How much did he save by paying the ready money? Ans. 141 dolls, 12 cts. 15. When sugar is sold for 12 dolls. 32 cts. per cwt, how much can I get, at that rate, for 6 dollars 16 cents ? Ans 56 lbs. 16. If 3 and 4 make 9, what will 8 and 6 make ? Ans, 18. 17. A loaded wagon was sent by Mr. Rabe to Wheeling, distant 40 miles, who arrived at Wheeling 16 hours after his departure from Washington. At what rate per hour did he travel? Ans. 2 miles 4 furlongs. 18. The same wagon returned empty in 10 hrs. 40 min. at what rate per hour did he travel ? Ans. 3 miles 6 furlongs. 19. If a family of 10 persons spend 3 bushels of wheat in a month, how many bushels will serve them, when they are so in family? Ans. 9 bushels. 20. What is cheese per cwt, when a pound costs 124 cts.? Ans. 14 dollars. 21. If lead is sold at 5 cts. a pound, what is 3 cwt. worth, at that rate ? Ans. 16 dolls. 80 cts. 22. If 100 dollars gain 6 dollars interest in a year, how much will 49 dollars gain in the same time? Ans. 2 dollars 94 cents. 23. How many reams of paper, at i dollar 6 dimes 6 cts. 1 dollar 9 dimes 7 cents, and 23 dimes 1 cent per ream, may I get for 1057 dolls. 32 cts. and of each an equal number? Ans. 178 reams. 24. When iron is sold for 67 dollars 20 cents a ton, what is that a pound? Ans. 3 cents. 25. How much will a grindstone, 4 ft. 9 inc. in diameter, and 9 inches thick, come to, at i dol. 10 cts. per solid foot? Ans. 13 dolls. 96 cts. + 26. What will 18 cwt. 3 qrs. 14 lbs. of tobacco come to, at 6 dollars the hundred pounds ? Ans. 126 dollars 84 cents. 27. If a man's yearly income be 1186 dolls. 25 cts. how much is it per week? Ans. 22 dolls. 814 cts. 28. If a man spends 3 dollars 25 cents a day, and saves 496 dollars 50 cents at the end of the year, how much is his yearly income? Ans. 1682 dolls. 75 cts. 29. The distance from here to Cambridge is 10 miles; now, how many steps will a man make in going to Cambridge, allowing he gains 18 inches each step; and how long will he be in going there, supposing he makes 2 steps in 3 seconds ? 35200 steps. Ans. Length of time, 14 hrs. 40 min. 30. I want to know the breadth of a river, running by the side of a castle, whose height I found to be 60 feet, from the surface of the water; and having a stick in my hand, just 3 feet long, I set it up perpendicular, and it cast a shadow at the same time of 5 feet. Now, the shadow of the steeple was 21 feet on the land, from the water's edge, where I was. What is the breadth of the river? Aps, 79 feet. 31. If 60 gallons of water in an hour fall into a cistern, containing 300 gallons, and by a pipe in the cistern, 30 gallons run out in an hour, in what time will it be filled ? Ans. 10 hours. 32. A and B depart from the same place, and go the same way; but A goes 5 days before B, at the rate of 20 miles a day; and B follows, at the rate of 23 miles a day. What distance must he travel, that he may overtake him? Ans. 500 miles. 33. If the schooltax in this state be 5 mills on a dollar, what must that man pay, who is taxed 820 dollars 50 cents? 34. How many more revolutions will the smaller wheels of a wagon make than the greater, in going a mile, the circumference of the larger ones 12 feet, and the lesser ones 9 feet? Ans. 146; more. 35. Bought a pipe of wine for 84 dollars, and found it had leaked 12 gallons. I sold the remainder at 12 cents 5 mills a pint. Did I save myself? Ans. I gained 30 dolls. 36. Two men depart from the same place at the same moment, and one goes due west 30 miles a day, the other due east 25 miles a day. How far are they apart the third day after their departure ? Ans. 165 miles. 37. How much corn, at 31+ cents a bushel, must I give for 150 bushels of wheat, at 56 cents a bushel ? Ans. 270 bushels. 38. What will 1 mile 6 furlongs 25 rods of the making of the turnpike road come to, at 2 dollars 3 dimes, and 250 mills a rod? Ans. 1491 dolls. 75 cts. 39. If 250 men in a garrison consume 54 barrels of pork in six months, how many barrels will a regiinent of 1000 strong consume in the same time? Ans. 216 barrels. 40. If 1 yard 2 quarters of cloth cost 7 dollars, what will an ell Flemish cost, at that rate? Ans. 3 dolls. 50 cts, 41. If a man's yearly income be 1000 dolls. and he spends 1 dol. 62 cts. a day, how much does he save at the year's end ? Ans. 406 dolls. 87 } cts. 42. If 2000 dollars were paid for 20 pieces of cloth, at the rate of 12 dollars 50 cents for every five yards, how many yards were in each piece, allowing them to measure alike? Ans. 40 yards. 43. What is the price of four pieces of cloth, containing 24, 26, 27 and 31 yards, at 2 dolls. 25 cts. the ell English? Ans. 194 dolls, 40 cts. 44. Bought three bales of gloves, the first bale contained 8 dozen dozen and 10 pairs, the second contained 7 score and 7 pairs, and the third contained a quarter of a dozen dozen and two pairs, at 25 cts. a pair. How much do they come to, and how many pairs had I? Cost $ 336 75 cts. Ans. 1347 pairs. 45. A merchant in Baltimore failed in trade, and owed me, at that time, 2500 dollars, for tobacco s sold him; but he sent me word, that his effects and outstanding debts, when sold and collected, will enable him to pay his creditors 75 cts. per dollar. How much then am I to receive for my tobacco debt, and how much do I lose by the merchant failing? Ans. I receive $1875, and lose $625. 46. A sets out from a certain place, and goes at the rate of 20 miles a day. Five days after, B sets out from the same place, and goes at the rate of 25 miles a day the same road. In how many days will he overtake A? Ans. 20 days. 47. If the earth, which is 360 degrees in circumference, turns round once in 24 hours, how far are the inhabitants carried round in an hour living at the equator, a degree there being 69} miles ? Ans. 1642 miles 4 furlongs. 48. Bought 3 hhds. of peach brandy, containing 60 gallons 3 quarts, 61 gallons 2 quarts, 59 gallons 1 pint, and 63 gal. lons 3 quarts 1 pint, at 6 dimes 40 cents for every 4 gallons. What is the whole amount? Ans. 61 dolls. $1. cts. 49. How much will a quarter section of land come to now, the congress price per acre being only 1 dollar 25 cents? Ans. 200 dollars. 50. If a man lays out 121 dollars 23 cents in tobacco, anıl thereby gains 39 dollars 51 cents, how much will he gain on 100 lbs. weight, which cost 6 dolls.? Ans. Idol. 954 cts. THE SINGLE RULE OF THREE INVERSE. This Rule teaches, by having three numbers given, to find a fourth, which will have the same proportion to the second, as the first has to the third. · When more requires less, or less requires more, the question is in this Rule; but when more requires more, and less requires less, the question belongs to the kule of Three Direct. RULE. State your question as in the Rule of Three Direct, and multiply the first and second terms together; then divide the product by the third term, and the quotient will be the answer, in the same name as the second number, EXAMPLES. 1. If 6 men can mow a meadow in 24 days, how many can mow the same in 4 days? Ans. 36 men, days. men. days. If 24 : 6 4 6 4)144 -36 men. Ang. NOTE. The product of the third nunber, multiplied by the answer, will be always equal to the product of the first multiplied by the second, in Inverse Proportion ; and ibe first cun.ber, multiplied by the answer, will be equal to the second multiplied by the third, in Direct Proportion. |