56

ment of which A advances 3, B, and C £140. How much paid A and B, and what part of the vessel had C ? and reduced to a common denominator become ? and 24, and 21+34=45; then the whole 56-45-11 C's part of the vessel. Then as £140 to £267 A paid, and 140:: 24 to £30515 B paid.

569

56

:

21

56

34. The third part of an army was killed, the fourth taken prisoners, and 1000 fled. How many were in this army? How many killed? and how many captives ?* +1 of the army, and 12-22, therefore, 1000 is of the army; then if I be 1000, how many is 13, or the whole?

Ans. 2400 in the army, 800 killed, and 600 prisoners. 35. There is a mast or pole which stands of its length in the mud, 12 feet of it in the water, and of its length in the air, or above water, what is its whole length ?*

36. What number is that which quotient will be 21 ?

Ans. 216ft.

being divided by the Ans. 153.

of them bear apples, 4

37. In an orchard of fruit trees, pears, peaches, and 50 of them cherries. How does the orchard contain ?

many trees Ans. 600.

38. There is a certain number which being divided by *, the quotient resulting multiplied by 3, that product divided by 5, from the quotient 20 being subtracted, and 30 added to the remainder, the half sum shall make 35. Can you tell me the number? Ans. 700.

39. A farmer being asked how many sheep he had, answered that he had them in 5 fields-in the first he had of his flock, in the second, in the third, in the fourth, and in the fifth 450. How many had he ?* Ans. 1200.

40. A gentleman divided his fortune among his 3 sons, giving A $9 as often as B $5, and to C but $3 as often as B $7, and yet C's dividend was $2584. What was the whole amount of the estate ? Ans. 19466,13+

41. A and B together, can build a boat in 18 days, and

*This and all those questions marked with an asterisk, may be solved by the rules of Position, or on general principles by fractions. And the scholar may, for practice, solve them by both methods. But he should be required to pay parficular attention to the method of solving by fractions, which is generally much preferable to that of position or supposition.

with the assistance of C, they can do it in 11 days. In what time would C do it alone? Ans. 28 d.

42. A and B laid out equal sums of money in trade-A gained a sum equal to of his stock, and B lost $225.— What sum did Then A's money was double that of B's.

each lay out?*

Thus the whole=4, and A gained +4, the amount of A's stock and gain together, which is double B's; then of, and taken from leaves, which B lost.Then as $225 :: to the answer.

Ans. each laid out $600.

43. If to my age there added be,

One half, one third, and three times three,
Six score and ten the sum will be,

What is my age ?

* tell it me. pray

1+1=5, and the whole +=. Therefore,

1

Then 121: 8 :

44. If A can do a piece of work in 20 days, B in 30, and C in 60 days, in what time will they all do it by working together?

45. What number is that which being increased by its, its, and 18 more, will be doubled ?*

1+1=2 and 1=1+3=1 and double 4-2 and consequently 18 is of the required number.

-1=1,

Ans. 72. be added

46. What number is that to which if of itself the sum will be 40?* 40 is of what number? Ans. 35. 47. What number is that, which being increased by its ,, and 2, and 14 more will be made 3 times as large ?* 14 of the required number.

Ans. 168:

48. A Stationer sold quills at 11s. per thousand, by which he cleared of the money; but growing scarce he raised them to 13s. 6d. per thousand; what might he clear per cent by the latter price? Ans. £96 7s. 3d

49. The hour and minute hand of a watch are exactly together at 12 o'clock. When are they next together?

The minute hand passes over 12 spaces while the hour hand passes over 1 space, consequently the minute hand

gains upon the hour hand 11 spaces in 1 hour; and it must gain 12 spaces in order to coincide with it.

Therefore, 11: 1 :: 12 Ans. 1h. 5m. 273s. Then if we multiply the above answer by 2, 3, 4, &c., it will show the times when the hands are next together.

50. A person being asked what o'clock it was, replied that it was between 3 and 4, and that the hands on his watch were exactly together. I demand how much it was past 3 o'clock ? Ans. 16m. 21s. 51. A gentleman left his son a fortune, of which he spent in three months; of the remainder lasted him 8 months longer, when he had only $2850, left. Pray what did his father bequeath him? Ans. $6650.

52. A father left his two sons (the one 11, and the other 16 years old,) 10000 dollars, to be divided so that each share being put at interest at 5 per cent might amount to equal sums when they would be respectively 21 years of age. Required the shares. Ans. $5454, and $4545.

B

53. A lets B have 120 gallons of brandy, worth 95cts. for $1,25 per gallon, of which B is to pay in cash. has paper worth $2 per ream, which he gives A for the rest of his brandy, at $2,50 per ream. of the bargain, and how much?

Which gets the best
Ans. A by 13,50.

54. Divide $600 among 3 men, in such a manner that as often as the first has $3, the second shall have $5, and the third $7. How many dollars will each receive? (See ex. 18.) Ans. A 120, B 200, and C 280.

55. A gentleman had £7 17s. 6d. to pay among his laborers to every boy he gave 6d., to every woman 8d., and to every man 16d., and there were for every boy, 3 women, and for every woman, 2 men. I demand the number of each? Ans. 15 boys, 45 women, and 90 men.

56. Bought a quantity of broadcloth for $2070, and if the number of dollars which it cost per yard, were added to the number of yards bought, the sum would be 351. What was the number of yards bought, and how many dollars was it per yard? (Solved by Prob. 6, page 188.)

Ans. 345yds. at $6 per yard. 57. Bought a quantity of cloth for £383 5s. and the difference between the number of shilling it cost per yard, and

the number of yards bought, was 344. I demand the number of yards bought, and the price it cost per yard. (Solved by Prob. 7, page 189.)

Ans. 365 yards, at 21s. per yard. 58. A farmer driving his sheep to market, was met by a person who inquired how many sheep he had; to avoid a direct answer, the farmer replied, if you multiply one-half and three-fourths of my number together, the product will be 864. Can you tell me how many sheep he had? (Solved by Prob. 1, page 194. Ans. he had 48. 59. Divide $500 between A and B so that A's share shall be as much as B's.*

60. What o'clock is it in the afternoon, when the time past from noon is equal to of the time to midnight.*

Ans. 26 minutes past 1.

61. A and B talking of their ages, A said that of his age was equal to of B's, and that the sum of their ages was 68. Required the age of each.

(Reduce the fraction to a common denominator, and the numerator will be the proportions, ex. 18.)

Ans. A's 36, B's 32.

62. William and Henry enter into partnership, and buy a stock of goods, and at the end of 12 months, having sold the goods, they find that they have gained at the rate of 200 per cent upon the prime cost; they then divide their gain between them in proportion to the purchase money paid by each, which was as 5 to 7; and Henry says to William, my part of the gain is really a handsome sum of money, and if I had as many such sums as your part contains dollars, I should then have $686000. Required the sum of money paid by each in purchasing the stock. (Solved by Prob. 2, page 195.)

Ans. William paid $350, and Henry $490.

AN

APPENDIX;

CONTAINING

USEFUL PROBLEMS IN THE MENSURATION OF

SUPERFICES AND SOLIDS.

SECTION I.-SUPERFICIES.

The area of every plain surface is conceived to be made up of a certain number of squares, either greater or less, according to the measure by which the dimensions are taken, which is generally in inches, feet, yards, rods, &c. A square inch means a space an inch long and an inch broad, in which depth or thickness is not considered; and so of square feet, yards, rods, &c. And the superficial contents, or area of any plain surface, is the number of square inches, feet, yards, rods, acres, &c., which it contains.

PROBLEM I.—To find the area of a Square.

RULE.

Multiply the side of the square into itself, and the product will be the area, or contents.

EXAMPLES.

1. How many square feet of boards are contained in the floor of a room which is 16 feet square?

Ans. 256. 2. How many acres are contained in a square field which measures 65 rods on each side? [Reduce the whole number of square rods to acres.] Ans. 26 acres 1 r. 25 rods. PROB. II. To find the area of a parallelogram, or long square.

RULE.

Multiply the length by the breadth, and the product will be the area.

EXAMPLES.

1. How many square yards of ground are contained in a garden which is 126 feet long and 65 feet wide? [9 sq. feet-1 sq. yard, therefore the sq. feet by 9.] Ans. 910 sq. yds.

2. How many acres are contained in a lot of land in the form of a long square, which is fifty-six rods in length and thirty-seven rods in width ? Ans. 12 acres 3 r. 32 rods. 3. How many feet in a board or plank 18 feet long, and 1 foot 6 inches wide?

By duodecimals, 18F 0'X1F 6'=27ft. 0', Ans.

By decimals, 1ft. 6in.=1,5ft. Then 18×1,5=27, Ans. Or, multiply the length in feet by the breadth in inches, and divide the product by 12. Thus, 18ft.×18in.÷12=27ft. Ans. as before,