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after sold them for $275; how much per cent. per annum did I gain by them ?
Ans. $40. 21. In what time will the interest of 872,60cts equal that of $15,25cts. for 64 days, at any rate of interest ?
Ans. 13167 days. 22. What sum of money will amount to $132,8lcts. 24m. in 15 months, at 5 per cent. per annum simple interest ?
Ans. $125. 23. A person possessed of of a ship sold of his share for $1260; what was the reputed value of the whole at the same rate ?
Ans. 5040. 24. Of my or of a farm I sell of f; what I then own is worth $185 ;--what is that part, and what the value of the farm ?
Ans. and the farm $1200. 25. What number is that to which if it of ys of be added, the total will be one ?
Ans. 3648 26. If of off of a ship be worth of of 11 of the cargo, valued at 40000 dollars; what is the value of the ship and cargo ?
Aps. $50744,81cts. + 27. A grocer would mix a quantity of sugar at 10d. per pound, with other sugars at 77d. 5d. and 4jd. per pound, intending to make up a compound worth 6d. per pound; what quantity of each must he take? Ans 13 it at 10d.
1ff at 74d. 14 at 5d. and 41 at 41d. 28. If 1000 men besieged in a town, with provisions for 5 weeks, allowing each man 16 ounces a day, were reinforced with 500 men more, and hear that they cannot be relieved till the end of 8 weeks; how many ounces a day must each man have, that the provisions may last that time?
Ans. 6 ounces. 29. Sound, not interrupted, is found by experiment to move uniformly about 1150 feet in a second of time; how long then after firing an alarm gun at Fort Independence, may the same be heard at Cambridge, taking the distance at 50 miles ?
Ans. 2624 seconds. 30. If I see the flash of a gun fired by a vessel in distres& at sea, which happens, we will suppose, at the instant of its going off and hear the report a minute and 3 seconds afterwards; how far is she off? Ans. 72450 feet.
81. An elm plank is 14 feet, 3 inches long ; what distance from the edge must a line be struck to take off a yard square ?
Ans. 711 inches
32. A man dying left his wife in expectation that a child would be afterwards added to the family, and in making his will ordered, that if the child were a son, f of his estate should belong to him, and the remainder to his mother; but if it were a daughter, he appointed the mother, and the child the remainder ; but it happened that the addition was both a son and a daughter, by which the widow lost in equity 2400 dollars more than if there had been only a girl ; what would have been her dowry, had she had only a son ?
Ans. $2100. 33. Having a piece of land 11 perches in breadth, I demand what length of it must be taken to contain an acre, when four perches in breadth require 40 perches in length to contain the same ? Ans. 14per. 3yds.
34. If a gentleman whose annual income is £1000, spends 20 guineas, each 21s., a week, will he fall in debt, or save money, and how much in the year ?
Ans. £92 in debt. 35. What sum of money will produce as much interest in 34 years, as $210,15cts. can produce in 5 years and 5 months ?
Ans. $350,25cts. 36. If $100 in 5 years be allowed to gain 820, 50cts. in what time will any sum of money double itself, at the same rate of interest ?
Ans. 2411 years. 37. What difference is there between the interest of $350 at 4 per cent. for 8 years, and the discount of the same sum, at the same rate, and for the same time!
Ans. $27,15cts. 38. If by selling goods at $2} per cwt. I gain 20 per cent., what do I gain or lose per cent. by selling at $21
Ans. $8 per cent. gain. 39. Required the length of a shore, which, strutting 11 feet from the upright of a building, may support a jamb 23 feet, 9 inches from the ground. Ans. 26ft 2in. +
40. A clears $13 in 6 months, B $18 in 5, and C 823 in 9, his stock being $72}; what, then, is the general stock?
Ans. $236,0941. 41. A person making his will, gave to one child 1 of his estate, and the rest to another; when these legacies came to be paid, the one turned out $600 more than the other : what did the testator die worth? Ans. $2000.
42. A father devised jg of his estate to one of bis sons and is of the residue to another, and the remainder to bis
per cwt. ?
widow for life; the children's legacies were found to be $257,163cts. different:-pray what sum did he leave the widow the use of?
Ans. $635,04 2,cts. 43. A had 12 pipes of wine, which he parted with to B at 41 per cent. profit, who sold them to C for $40, 60cts. advantage ; C made them over to D for $605,50cts., and cleared thereby 6 per cent. :-how much a gallon did this wine cost A ?
Ans. 336459cts. 44. Laid out $ 165,75cts. in wine at ?11cts. a gallon; some of which receiving damage in carriage, I sold the rest at 31 cts. a gallon, which produced only $110,831 cts. ; what quantity was damaged ? Ans. 430gals
45. A young hare starts 40 yards before a greyhound, and is not perceived by him till she has been up 40 seconds; she scuds away at the rate of ten miles an hour,
; and the dog, on view, makes after her at the rate of 18; how long will the course hold, and what ground will be run over by the dog ? Ans. 60,5 sec. and 530 yds. run.
46. If I leave Hallowell at 8 o'clock on Monday morning for Newburyport, and ride at the rate of 3 miles an hour without intermission; and B sets out from Newburyport for Hallowell at 4 o'clock the same evening, and rides 4 miles an hour constantly: supposing the distance between the two towns to be 130 miles, whereabout on the road shall we meet ?
Ans. 693 miles from Hallowell, which will be in Saco.
47. X, Y, and Z, can, working together, complete a staircase in 12 days; Z is man enough to do it alone in 24 days, and X, in 34; in what time, then, could Y get it done hiinself?
Ans. 813 days. 48. A and B together can build a boat in 18 days, and with the assistance of C, they can do it in 11 days; in what time then, would C do it by himself?
Ans. 289 days. 49. Laid out in a lot of muslin £500, upon examination of which 3 parts in 9 proved damaged, so that I could make but 5s. a yard of the same ; and by so doing, find I lost £50 by it; at what rate per ell Eng. am I to part with the undamaged muslin, in order to gain £50 upon the whole ?
Ans. 11s. 74d. 50. If the sun move, every day, one degree, and the maon thirteen; and, at a certain time, the sun be at the
beginning of Cancer, and, in three days after, the moon at the beginning of Aries; the place of their next following conjunction is required. Ans. 10° 45' of Cancer.
51. A person being asked the time of day, answered, it is between 4 and 5 ; but a more particular answer be ing required, he said, that the hour and minute hands were then exactly together ; what was the time?
Ans. 21 min. past 4. 52. What weight, hung at 70 inches' distance from the fulcrum of a steelyard, will equiponderate a bhd. of to. bacco, weighing 950 16. freely suspended at 2 inches' distance on the contrary side? Ans. 27th. 2oz. 44drs.
53. If two places lie so much due east and west of each other, that it is found, by observation, to be noon at the former 2 hours, 6 min. and 30 seconds sooner than at the latter; how many degrees are they apart !
Ans. 31° 37' 30 seconds. 54. If Paris, in France, be in 2° 20° east longitude from Greenwich, and Hallowell in 69° 42' west longitude from Greenwich; when it is noon at Paris, what time of day is it at Hallowell ?
Ans. 7h. 11m. 52s. in the morning.
MEASUREMENT OF GRINDSTONES. GRINDSTONES are sold by the stone, and their contents found as follows ;*
RULE. To the whole diameter add half of the diameter, and multiply the sum of these by the same half, and this product by the thickness ; divide this last number by 1728, and the quotient is the contents, or answer required.
E.XAMPLES. 1. What are the contents of a grindstone 24 inches diameter, and 4 inches thick ?
24 + 12x12x4
=l stone. Ans.
1728 2. What are the contents of a grindstone 36 inches diameter, and 4 inches thick :
Ans. 24 stone. * 24 inches in diameter, and 4 inches thick, make a stone.
MENSURATION of Superficies and Solids.
Section 1.-OF SUPERFICIES. Superficial measure is that, which relates to length and breadth only, not regarding thickness. It is made up of squares, either greater or less, according to the different measures by which the dimensions of the figure are taken or measured. Land is measured by this measure, its dimensions being usually taken in acres, rods, and links. The contents of boards, also, are found by this measure, their dimensions being taken in feet and inches. Because 12 inches in length make 1 foot of long measure, therefore 12x12=144, the square inches in a superficial foot, &c. CASE 1.-To find the Area of a square having equal sides.
RULE.--Multiply the side of the square into itself, and the product will be the area, or superficial content, of the same name with the denomination taken, whether inches, feet, yards, rods and links, or acres.
EXAMPLES. 1. How many square feet of boards are contained in the floor of a room which is 20 feet square ?
20x20=400 feet, the Answer. 2. Suppose a square lot of land measures 26 rods on each side, how many acres does it contain ?
26 x 26 As 160 square rods make an acre : therefore -=4ac. 36 ro.
160 Ans. Case 2.--To measure a parallelogram or long square.
Rule.-Multiply the length by the breadth, and the product will be the area, or superficial content, in the same name as that, in which the dimension was taken, whether inches, feet, or rods, &c.
EXAMPLES. 1. A certain garden, in form of a long square, is 96 feet long, and 54 feet wide; how many square feet of ground are contained in it? 96x54=5184 square feet. Ans.
2. A lot of land, in form of a long square, is 120 rods in length, and 60 rods wide; how many acres are in it ? 120x60=7200 sq. rods. And 7200--160=45 acres. Ans.