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much more profitable is the making of cheese than butter, the price of butter being 25 cts. per pound, and that of cheese 87 eta. per pound? A. $110,40.
44. If a field will feed 10 cows four weeks, how long will it feed 40 cows? A. 1 week.
45. A man bought a cask of wine, containing 126 gallons, for $15, and sold it at the rate of $2,75 per gallon; how much was nis whole gain? how much per gallon? and how much per cent. ? A. His whole gain, $31,507 per gallon, $,25; then, 25.=01 per cent.
46. The rent of a certain farm is $500; the tenant employs ? men; to each he pays $11a month for 8 months-184 ; also a boy by the year, who is to have 2 suits of clothes, each wortb $8,75-1750, besides his board, while attending school, 3 months, or 12 weeks of the year, whieh is worth $,93 per week-1116; in the course of the year, the tenant loses 40 good nierino sheep, valued at $5 per head-200; the skins brought him $1,12 apiece-45; the other expenses of the year are calculated to average about $,39 per day-14235; the sales of the farm aro as follows, viz:-
1000 bushels of Potatoes, .... at $0,42 per bushel,-420,
• • pround, 575,
$0,43 . . bushel, 860,
... 1750 400 pounds. . Merino Wool, . . . $0,45 • . pound, 180, and 20 calves, at $4d per head-90; he carries 70 barrels of oto der to the distillery, for one half of which he is to receive 1 qt. of cider-brandy for 4 qts. of cider; the rest brings him $1,13 per barrel-3955; how much cider-brandy will he receive and how much will he clear, after deducting all the expenses of managing the farm, including the rent and loss, froni the total amount of sales? A $1338,57; 1102qts. cider-brandy.
47. What difference is there between the compound interest of $10000 for 8 years, and the simple interest of the same sum for the same time? 1. $1138,48.
48. What is the difference between the compound interest of $500 for 4 years, and the discount of the saino sum for the same time? Å. $34,403.
49. What is the difference between the amount of $1800, at compound interest, for 3 years, and the present worth of ibe same sum for the same time. A. $618,405.
50. If 120 gallons of water, in one hour, fall into a cistern containing 600 gallons, and, by one pipe in the cistern, 35 gal. fons run out, and, by another pipe, 65 gallons run out, in what time will the cistern be filled ? A. 30 hours.
51. A certain clerk, in a country store, purchased the whole stock in trade, the quantity and price being as follows:
20 2 hhds. of Rum, .
per gallon,. 3276 1 hhd. of Molasses,
1512 1 bbl. of Brandy, lacking 5 gals. . $1,12
2968 2 bbls. of Brandy, ..
7308 1 pipe of Wine, lacking 15 gals. $0,85
9435 do... do. ........... 81,00 .
252 4 bbls. of Gin,....
7560 bbl. of Vinegar, ........ $0,25 .
5906 40 cinpty Barrels, ....
30 $3 empty logsheadls, ..
7056 2 pieces of Calico, 14 yds. each, $0,22 per yard, . 616 1 piece of Silk,. . 28. ...... $0,89
2492 ... Cotton, 11 ..
..$1,14 apiece, ..
1596 14 Hoes, ..
1162 12 Axes, ..
1404 15 Axe-helves,...
105 27 wooden Pails,
621 .. Tubs,
2070 10 Kettles, ..
2950 2 dozen of Knives, .
. $0,50 ......
follows: his services for the two last years, at $26 por month, turned in a note on James Spencer, of 500 dollars, with 5 year' compound interest due on it-6691 12; and, for the balance, he was to give his note, payable in 6 years from the date of 'the transaction, without interest: now the question is, what sum of ready money will discharge said note A. $93,657. .
After the clerk had purchased the above stock, and settled for the same, he commenced business for himself. The rent of his store costs hiin $29 a year; his clerk-hire $27,814 precisely, in addition to which is the interest of his capital, $1420,35, (that is, the interest of the amount of stock, after the 15 per cent. is deducted, $85221). He next considered whai price he must put on each article, to make a certain per cent He recollected ihat the goods were already cated in the inven. tory at 15 per cent. more than their actual cost. Now, said he, if I can make 5 per cent. in adyance on their present valuation, clear of all expenses, I shall be satisfied. The question, then, is, at what price he must mark each article, commencing with the first on the inventory, so as to clear the 5 per cent.
The pupil will find, by calculation, that the expenses amount to cent. on the actual cost of all the articles; this, added to the 5 per cent., makes 15 per cent, advance ; that is, each article must be marked 15 per cent. highet than its present valuation in the inventory. The answer to each follows in the same order as the articles stand in the above inventory, commencing with the 3 bbls. of sugar, and finding the selling price of each per ib., &c.
Note. In marking goods, it is customary to neglect the mills, if under 5
exactly 5, add of a cent, and if over 5, add 1 cent to the cents.
Snuff, .... 41 per te
llats,. ... 249 each. Geography, 138.
Whipg, ..131 exch,
52. Bought 42 gallons of rum, for $37,80; how much wates must be mixed with it, that it may be afforded for $,80 pes gallon?
$,80 : $37,80 :: 1 gal : 471 galls.; then, 471 = + 51 galls., Ans. 53. A thief, having 30 miles the start of an officer, males of at the rate of 8 miles an hour; the officer presses on afer him u the rate of 10 miles an hour: how much does ho gain on the
Chief in one hour? how long before he will overtake the thief!
54. A person, looking at his watch, was asked what o'clock
. 55. At 12 o'clock the hour and minute hands of a clock are i exactly together; when will they be together again?
Ans. 1 h. 5 m. 27 sec. 56. If 10 men can perform a piece of work in 25 days, how finany men will accomplish another piece of work, four times as a large, in a fifth part of the time? Å. 200.
57. A can do a piece of work in 8 days, and B in 12; in what time would both finish it by working together? 6 Days. Day. Work. Work. SI 8:1:: 1 :$ ft + tk= Then, i't.1..1:45, A
12 : 1 :: 1 :
58. What number is that, from which if you take 1, the re mainder will be 1? td=, Ans.
59. What number is that, from which if you take y, the re wainder will be ? Ans..
60. What number is that, from which if you take f of 1 of 2, the remainder will be $? Ans. * =17
61. What number is that, which, being divided by 3, the quotient will be g? 4. 24.
62. What number is that, which, being multiplied by $, the product will be 3!? A. 3 . . 63. What number is that, from which if you take of itself, the remainder will be 12?
1, or $,-=t, remainder. I'non, the remainder 12, being 4 x 12 = A uimos greater than the remainder }, the number itself will be 48 times greater Vaan I. A. 48.
64. What number is that, to which if you add s off of itsell, the sum will be 39 ?
for = r, and the nuinbor itsoll 18; then, to +18 = 18; if to the whole number 1 of fe of it he addod, the sum will be fi consequently 39 is 18 of tho nurabor. Ans. 30.
05. What number is that, to which if you adds of itself, the guin will be 18 ? A. 12.
66. A owns } of a vessel, B, C$, and D the remainder; D's part is $100: can you tell me how many dollars is each man's part, and what part of the vessel D owns ?
Ans. A's part, $100; B's, $200 ; C's, $400; and D'a part in de
67. There is a beam, te of which is in the ground, 16 in die water, and the rest, being 2 feet, out of water; how long is the beam? A. 16 feet.
68. The third part of an army was killed, the fourth part taken prisoners, and 1000 fled; how many were in this arnıy? how many killed ? how many taken captives?
5+=12, of the whole army; then, as Iz more makes 13, or the whole army, te=1000; and if : be 1000, how much is 13, or the whole? Ans. 2400, the whole army; 800 killed, 600 cap.ives.
69. Suppose that there is a mast erected, so that of its length stånds in the ground, 12 feet in the water, and of its length in the air, or above water; I demand the whole leagth
Reducing the fractions to the least common denominator, gives 2 + tk = t; therefore 12 feet=ts. A. 216 feet.
70. In an orchard of fruit-trees, of them bear apples, & pears,
plums, 40 of them peaches, and 10 cherries; how inany trees does the orchard contain ? 's=50 + 10. Ans. 000.
71. A man spent one third of his life in England, one fourth in Scotland, and the remainder, which was 20 years, in the United States ; to what age did he live? A. 43 years.
72. The number of scholars in a certain school is as follows: of the pupils study geography, $ grammar, 4 arithmetic, and jo learn to read; what number is pursuing each branch of study? A. 30 in geography, 80 în grammar, 120 in arithmo tic, and 10 learn to read.
13. The double and the half of a certain number, increased by 74 inore, make 100; what is that number? A. 31.
74. A man, having purchased a drove of cattle, was driving them to market, when he was met hy a gentleman, who in. quired of him where he was going with his 100 head of cattle ? Sir, said he, I have not near 100, but if I had as many more as I now have, . as many inore, and 7 cattle and ), I should have a hundred. How many had he ? A. 37.
75. Five eighths of a certain number exceeds of the same aumber by 36; what is that number?
*- = /; hence 30 is a's of the number sought. A. 160..
76. What number is that, which, being increased by $ $ und of itself, the sum will be 131 ? Ans. 73797
The eleven foregoing questions are usually performed by a rule called Position, but this method of solving them by frac wons is preferable.
7. A hare starts up 12 rods before a hunter, and scudo away