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6. If 9 bushels of wheat cost $12; what cost 36 bush els ?
Ans. $48. 7. I! 36 bushels cost $48; what will 9 bush. cost? Ans. $12.
8. If 60 bushels of flax seed cost 45 dollars; what will i bushel cost?
Ans. ,75cts. 9. If one bushel cosi 75 cents; what will 60 bushels cost ?
Ans. $45. 10. If 48 dollars will buy 12 yards of cloth; how many yards will 36 dollars buy?
Ans. 9 yards. 11. If 36 yards of broad cloth be worth 144 dollars; what will 9 yards be worth?
Ans. $36. 12. If 28 pounds of butter cost $2,52 cents; what will 7 pounds cost ?
Ans. ,63cts. 13. If 63 bushels of oats cost $20,16cts.; what will 12 bushels cost?
Ans. 83,84cts. 14. At $1,25 per head; what will 40 sheep, cost?
Ans. $50. 15. If 50 dollars will buy 40 sheep; how many sheep will 112 dollars and 50 cents buy?'
Ans. 90. 16. What will 300 acres of land cost, at ten dollars and fifty cents per acre?
Ans. $3150. 17. If 300 acres of land cost 3150 dollars ; what cost 1
Ans. $10,50cts. 18. If Icwt. 2qrs. of beef cost $8,40cts. ; what is the value of 3cwt. Iqr. 121b. ?
Ans. $18,80cts. Cut. gr. $ets. Cut. 97. lb,
When the 1st and third 1 2 : 8,40 :: 3112
terms are of different de4
nominations, the better 6 13
way is to state the ques28 28
tion, and then perform
the reduction, because the 48 116
whole work will then 12 26
show itself together. 168 lb, :
NOTE--The learner 150,40
must be careful in stating 3008 cls.
questions, that the first
and third terms be alike; 168)3158,40(18,80 Ans.
that is, if the first term 168
be weight, the third term 1478
must be weight; if the 1344
first term be money, the 1344
third must be money; and 1344,
the middle or second term!
must be the same kind of the answer sought; that is, if weight be required for the answer, the second term must be weight, if money be required for the answer, che second term must be money. 19. If a man's yearly income be 438 dollars; what is that
Ans. $1,20cts. 20. If a man's wages be 162 dollars a year; what is that per calendar month?
Ans. $13,50cts. 21. If 4yds. 24rs. cost 19 dollars; what will 3yds. 3qrs. cost?
Ans. $15,83cts. 3m. 22. If 2yds. 3qrs. cost $6,60cts.; what will 11 yards cost?
Ans. $26,40cts. 23. If 11 yards cost 26 dollars 4Octs.; what will 2 yards 3qrs. cost ?
Ans. $6,60cts. 24. If a man spend 1 shilling and 6 pence a day; how long will £27 7s.6d. last him?
Ans. 1 year, or. 365d. 25. A merchant failing in trade, compounds with his creditors for 56 cents on the dollar, and at that rate, pays 2840 dollars 12 cents; what was his debt ? Ans. $5071,64,2m.
26. Suppose the clothing of a regiment of 750 men amounts to £2381 5 shillings; what will the clothing of a body of 3400 men amount to?
Ans. £10795. men. . €
The learner will recollect, 750 : 2381 5 :: 3400 that when the second term is 20
expressed in different denomi47625
nations, it must be reduced to 3400
the lowest denomination men19050000
tioned, and the quotient or an
swer will be of the same name 142875 210
of the second term, to what750/161925000(2159010
ever it is reduced. 1500 £10795 NOTE.- Whenever there is 1192
a remainder, after dividing by 750
the first term, and the second 4425
term has not been reduced to 3750
the lowest denomination, the
remainder must be reduced to 6750
the next inferiour denomina6750
tion, and the division continued, 000
the same as in Compound Di."
27. What will be the yearly income from 173 acres, 2 roods, 14 poles of land, at the rate of £1 78, 8d. per acre ?
Ans. £240 25. 72.d. 28. If 9cwt. of sugar cost £54; what will 7cwt. 3qrs. 14lb. cost?
Ans. £47. 58. 29. A owes B $350, but B compounds with him for 65 cents on the dollar; what must B receive for his debt ?
Aps. $227,50cts, 30. A bankrupt owes 1250 dollars, and his money and ef fects amount to $750,50 cents; what is a creditor entitled to, whose demand is 40 dollars ?
Ans. $24,01ct. 6m. 31. If a person's income be $1877,50cts, a year; how much may he spend each day, to save, at the year's end, $600 ?
Ans. $3,50cts. 32. If a man receive 7 dollars interest a year, for the use of 100 dollars; what should he receive for the use of 375 dollars, the same time?
Ans. $26,25cts. 33. If the interest of 375 dollars for one year, be $26,25cts.; what will it be for 19. days?
Ans. $1,36cts. 6m. 34. Bought 10 pieces of cloth, each piece..containing 254 yards, at $2,50cts. per yard; what did the whole come to ?
Ans. $643,75cts. 35. Bought 120 gallons of brandy for $187,50cts.; how much water must be added to the brandy, to reduce the first cost to $1,25cts.?
Ans. 30gal. NOTE.- When the given number is in barrels, bales, packages, or pieces, each containing an equal quantity, reduce the quantity contained in one, to its lowest denomination, and then multiply by the given number of packages or pieces. If the given number of barrels, bales, pieces, &c. be of unequal content, put the separate content of each' under one another, as in Compound Addition, then add them, and their sum will be the whole quantity.
36. Bought 3 pieces of cloth, containing 36, 34, and 28} yards, at $2,50 per yard; how much did the whole amount to ?
Ans. $247,50cts. 37. Bought 3 hogsheads of rum, containing 60, 627, and 61 gallons, at 90 cents per gallon; what did the whole come
Ans. 8165,60cts. 38. * Suppose a freight boat leave Utica for Albany, 12 hours before a packet boat, and go at the rate of 2} miles an
* This sum will require two statements; one to ascertain the time, and the other the distance.
hoúf, thề packet follows at the rate of 4 miles an hour; in what time, and at what distance will the packet overtake the freight boat?
The packet will overtake the freight boat, in 20h. Ans.
39. A, leaves the city of New York, to go to Montreal, in Lower Canada, and travels at the rate of 35 miles a day; B, at the same time, leaves Montreal to go to New York, and travels the same road, at the rate of 30 miles a day; how far from the city of New York will they meet, allowing the distance to be 390 miles from
Ans. 210 miles
* Ans. 336 rods. 41. If 80 gallons of water, in one hour, be conducted into a cistern which will hold 400 gallons, and a conductor con. vey 30 gallons from the cistern in an hour; in what time will it be filled ?
Ans. 8 hours. 42. The valuation of the property in a certain town, according to the town's inventory, is $610;000, and the tax levied on that town, is $3050; what is A's 'tax, whose estate according to the inventory is valued at $1500?
Ans. $7,50cts. Note.-As the valuation of the whole property in the town, is to the whole lax, so is the valuation of each man's estate, to his tax.
43. If a tax of $650 be laid on a certain school district, for erecting a school house, and the inventory of all the estates, in that district, amount to $130,000; whät must A pay, whose estate is $2500 ?
Ans. $12,50cts. 44. The time made out by the inhabitants of a certain school district, amounts to 3040 days, during the winter, and the teacher is to have $75 for his services; what must A pay, who has sent 80 days to the school ? Ans. $1,97cts. 3m.
15. How many yards of carpeting that is half a yard wide, will cover a room 18st. wide, and 20ft. long? Ans. 80yds. NOTE.-To obtain the surface of a plane, as a floor, field, 4-c. Multiply the length by the breadth, and the product will be the surface; then as the number of square feet in a yard of the carpeting which is 4,5 feet, is to one yard, so is the number of square feet in the floor, to the number of yards required.
46. How many bricks that are 4 inches wide, and 8 inches long, will lay a floor sixteen feet wide, and twenty feet long?
Ans. 1440 bricks. 47. If a staff six feet in length cast a shadow of four feet, what is the height of a tree, whose shadow at the same time measures 125 feet?
Ans. 187 feet 6 inches. 48. A merchant bought 8 hogsheads of brandy, for 950 dollars; he paid for the freight $100, for the duties and other charges $50; and he wishes to gain $100; how must he sell it per hogshead ?
Ans. $150. Note.--It is just the same as if the merchant had, at first, paid out for ihe brandy the amount of the freight, duties, and other charges, together with the gain and the first cost, and then should wish to know what it cost him per hogshead.
49. A merchant bought 16 hogsheads of wine, at the rate of £87 13s. 6d. per hogshead, New-York currency; how many dollars will pay for it, in federal money? Ans. $3507.
59. Suppose a merchant pay !2$. 6d. New England cur. rency, a gallon, for wine; what would 1000 gallons amoun; to, at that rate, in federal money ? Ans. $2083,33cts. 3m.
51. Bought 300 Ells English, for 500 dollars, but being damaged, I am willing to lose 50 dollars by the sale; how must I sell it per yard?
Ans. $1,20cts. 52. If I þuy glb. of coffee for $1,08 cents; how many pounds can I buy for 9 dollars ?
Ans. 75lb. 53. A gentleman being asked what hour of the forenoon it was, answered, it is between 8 and 9, and the minute and hour hands are together ; what was the exact time?
Ans. 43 ji minutes past 8. NOTE.-The motion of the minute hand, to that of the hour hand, is as 12 to 1, therefore 12—1=11; then as 11 is to 8, so is 12 to the an.
THE RULE OF THREE INVERSE. This Rule, like the Rule of Three Direct, is properly an application of Compound Multiplication and Compound Division, and may like Direct Proportion be reduced back to those rules. This rule is sometimes called Indirect or Inverse Proportion.