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many leaps must the hound take to overtake the hare?

32. If a flag-staff 30 feet in height at a certain hour casts a shadow of 20 feet, what must be the height of that staff which at the same time casts a shadow of 25 feet?

33. Two men have a flock of sheep; A has 15 more than half of the number that B has, and both have 54; how many have each?

34. Smith and Robinson go into partnership, each putting in $300; afterwards Smith puts in twice as much, and Robinson 3 times as much as before; what share of the capital has each contributed?

35. The sum of two numbers is 24, and 3 times the first, less twice the second, is 17; what is each?

36. The circumference of a circle is 22 inches; what is its area?

NOTE. The area of a circle is equal to half the diameter multiplied by half the circumference.

37. How much greater area has a circle 22 inches in circumference, than a square of the same perimeter?

38. Bought 60 apples at 5 for 2 cents, and sold half of them at 2 for a cent, and half at 3 for a cent; how much was the gain?

39. A man being asked what time it was, answered that the time past noon was of the time past midnight; what time was it?

40. A man being asked the time of day, answered that the time past noon was equal to of the time past midnight; what time was it?

41. A man said that of the time past noon was equal to of the time to midnight; what was the hour?

42. A and B start from the same point, and travel in the same direction around a square, each side of which measures 5 miles; A travels at the rate of 4 miles an hour, and B at the rate of 3 miles an hour; in what time will they be together again? How many miles will each have travelled? How many times will each have been around the square?

43. There is a cask containing 50 gallons of wine; if one half of the wine be drawn off and an equal quantity of water be added, and then one fifth of this mixture be drawn off and the same quantity of water poured in, how many gallons of wine and how many of water are there in the cask?

44. A cask capable of holding 75 gallons, contains 50 gallons of wine; if enough water be poured in to fill the cask and one third of the mixture be drawn off, and then 10 gallons of water be poured in and one sixth of the mixture drawn off, how many gallons of wine and how many of water remain in the cask?

45. A wolf can eat a sheep in 2 days; a hound can eat it in 3; and a mastiff, in 4 days; after the wolf has eaten of a day and the hound of a day, how long will it take the hound and mastiff together to eat what remains?

46. A bought a horse for 25 per cent. less than his real value, and sold him to B for 25 per cent. more than his value; how much per cent. did A make on his purchase? How much per cent. would B lose were he to sell the horse for the same price that A gave?

47. A lady has 2 silver cups, and but one cover for both; the cover weighs 10 ounces; now, if the cover be put on the first cup, it will make the weight double that of the second, and if the cover

be put upon the second, it will make the weight triple that of the first; what is the weight of each?

48. There is a bin containing 30 bushels of wheat; if I take from it 10 bushels and add 10 bushels of rye, then take away 10 bushels of the mixture and add 10 bushels more of rye, then take away 10 bushels of this mixture and add 10 more of rye, supposing the wheat and rye to have been thoroughly mixed each time, how many bushels of wheat, and how many of rye would the bin contain?

49. If I should each time add the 10 bushels of rye before taking out the 10 bushels of the mixture, and perform the operation three times, as in the last example, how many bushels of each would remain in the bin?

50. If a merchant purchase goods for cash to the amount of $500, when money is worth 2 per cent. a month, what sum will he gain by selling the goods at the end of 4 months, but on 3 months' credit, at an advance of 20 per cent. upon the cost?

51. A father said to his son, "4 years ago I was 3 times as old as you, but 8 years hence I shall be 2 times as old as you;" what was the age of each?

52. A gentleman let of his money at 5 per cent., and the remainder at 6 per cent.; the interest amounted to $90; what were the sums let?

53. After spending of my money, I found if I had spent $1 less, I should have spent just of my money; how much did I have?

54. A grocer has two kinds of tea, one of which is worth 40 cents a pound, and the other 50 cents a pound; how many pounds of each must be taken to form a chest of 40 pounds, which shall be worth 44 cents a pound?

55. The sum of three numbers is 18, the sum

154

GREENLEAF'S MENTAL ARITHMETIC.

of the first and second is equal to the third, and half the sum of the first and third is equal to the second; what are the numbers?

56. A farmer employed 3 men and 3 boys one day for $5, and another day, at the same wages, 4 men and 6 boys, for $8; what was the daily wages of each?

57. What number is that to which if 3 and 14 be separately added, the first sum will be second?

of the

58. Three men, A, B and C, each, have a sum of money in their pockets; A has $3, A and C together have 3 times as much as B, and B and C together have 11 times as much as A; how much have B and C respectively?.

59. Smith, Jones and Brown, each, have a sum of money at interest at 5 per cent., and these sums are to each other as, and, respectively; the annual income of the three sums taken together is $90; what is the principal that each one has at interest?

60. Three men hired a pasture for $76; at first A put in 4 horses and 8 cows; B 6 horses and 12 sheep; afterwards, when the grass was half eaten up, C put in 24 sheep; now, supposing every horse eats, in a given time, as much as 4 sheep, and every cow as much as 3 sheep, what ought each man to pay?

61. Robinson, Savage and Harrison, agree together to do a piece of work; they are to receive for it $200, to be divided in the proportion of 5, 4 and 3, respectively, for the same amount of work; but Robinson, whose labor is worth most, is absent

of the time, and Harrison, whose labor is worth least, is absent of the time; how should the money be justly divided among them?

THE END.

SERIES OF MATHEMATICS.

THE Publishers of this Series, in its present revised and much improved form, would call the attention of Teachers, School Directors, and others interested, to its several important distinctive characteristics:

The ARRANGEMENT of its several parts and subjects is lucid, progressive, and strictly philosophical.

The RULES, DEFINITIONS, and ILLUSTRATIONS, are expressed in language, simple, clear, concise, and accurate.

The PROBLEMS are of a practical nature, tending to interest the pupil, exercise his ingenuity, and secure useful mental discipline.

It is a CONSECUTIVE SERIES, adapted to Primary, Intermediate, Grammar, and High Schools; and is in accordance with the best modern methods of instruction.

The MECHANICAL EXECUTION is neat and durable, an important consideration, too often disregarded.

I. THE NEW PRIMARY ARITHMETIC Constitutes attractive and interesting First Lessons in numbers, and contains all the pupil needs as preparatory to the next book in the series.

In order that the reasoning of some of the principal processes might be the more apparent to the beginner, pictures of objects have been, to some extent, introduced. After these, counters are employed, as unit marks; and then follow lessons without any such aids, that the learner may early acquire the habit of depending upon mental resources alone for the solution of problems.

II. THE INTELLECTUAL ARITHMETIC, As an advanced course of exercises, inductive and analytic, it is thought, will fully meet the requirements of the highest standard of mental culture. It has been the constant aim of the author, in its preparation, to unfold inductively the science of numbers in such a series of progressive intellectual exercises as should awaken latent thought, encourage originality, give activity to invention, and develop the powers of discriminating justly, reasoning exactly, and of applying readily results to practical purposes. The advanced exercises in the fundamental processes of the science, given toward the end of the book, constitute a feature peculiar to this work.

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