Page images

2. Required the superficial contents of a walnut board, 11 feet 4 inches long, and 1 foot 6 inches broad. Ans. 17 ft.

3. What is the solid content of a load of wood, measuring 6 feet 6 inches in length, 3 feet 4 inches in width, and 3 feet 6 inches in height?

Ans. 75 ft. 10 in. 4. How many yards of yard wide paper will it take to paper a ceiling 47 feet 6 inches long, by 25 feet 6 in. wider

ft. in. ft. in. ft. in.
47 6 x 25 6 1211 3
ft. in.

yds. ft. Then 1211 3 ; 9=134 5. Answer. 5. A mahogany board measures 16 feet 10 inches, by 3 feet 2 inches—What is its content? Ans. 53 ft. 3 in. 8''.


1. There is a square pavement, containing 110889 square stones, all of the same size-I demand the number contained in one of its sides.

Ans. 333. 2. If 40 yards of broadcloth cost $240, what must it be sold at per yard, to gain 20 per cent. by the whole ?

Ans. $7.20. 3. If 12 apples are worth 21 pears, and 3 pears cost one cent, what is the price of 100 apples ? Ans. 58} cts.

4. A gentleman at his decease left $3000 to his 3 sons, whose ages were as follows: A. 18 years, B. 19 and C. 20 years; the guardian had directions to divide this sum in such a manner that the share of each, by being put to interest at 6 per cent. should be equal when they should respectively arrive to the age of 21 years—I wish to know how much each must receive at this age; also the sum bequeathed to each.

r Each must receive $1117.86.

Bequeathed to A,

947.33. B, 998.09.

C, 1054.58. 5. A. and B. jointly purchase 300 acres of land for $600, each paying $300: when they came to divide the land between them, it was agreed upon, that A. should have his choice, and the part he took was valued at 75 cents per acre more than


B's I wish to know the price per acre of each one's land, and the number of acres falling to each.

Rule for solving all questions of this nature, 1. Divide the sum paid by each, by the whole number of acres, and add the quotient to one half of the difference in the price per acre, and reserve the number.

2. Multiply the sum paid by each by the difference in the price per acre; divide the product by the whole number of acres, and deduct the quotient from the square of the reserved number; then extract the square root of this remainder, and add the root to the reserved number, and the sum will be the value of A's land per acre.

3. Deduct the difference in the price per acre of their land, from the value of A's land per acre, and the remainder will be the value of B's land per acre.

4. Divide the sum paid by each by their respective prices per acre, and the quotients will be the number of acres falling to them respectively.

Note. This rule applies to all questions of the above nature, whatever the articles purchased may be, if the name of the article or articles purchased be understood, and used instead of acre or acres. 300) 300 2).75 difference in price.

300 sum paid by each. 1 .375

.75 difference in price .375

1.375 reserved number.


1.890625 square of the reserved number.


300:-2.443 = 122.8 A. 1.140625(1.068

300:- 1.693 = 177.2 B. 1

1.375 reserved number.



2.443 Ans. Price of A's land.


2128)17025 1.693 price of B's land.




[ocr errors]

6. Two drovers, A. and B. purchased 100 cattle between them for $2400, each paying $1200; they divided them between them in such a way that A's stood him in $10 a head more than B's I wish to know what each of their cattle stood them in per head, and how inany fell to each.

CA's, $30.00 per head.

A had 40 head.

B В 60 7. A. B. and C. wrought 365 days between them, at the following wages, viz. A. 50 cents, B. 60, and C. 70 cents per day; they each wrought such a length of time as to receive the same wages,—I wish to know the amount of each one's wages and the time he wrought.

Each received $71.635.

A. wrought 143.27 days.


102.34 Rule for solving all questions of this nature, whether the

number of persons be three or more. 1. Take the continued product of the wages and time for a dividend.

2. Leave out the daily wages of one and multiply the wages of the others continually together, and thus continue leaving out the wages of one and multiplying the others, until the wages of each are respectively left out, and the others multiplied together, then add together these products for a divisor.

3. The quotient will be the amount of each one's wages for the time he wrought.

4. Divide this quotient by each ones daily wages, the quotient will respectively be the time each wrought.

8. A person willing to distribute some money among some indigent persons, wanted 20 cents to give them 20 cents a piece he therefore gave them 19 cents a piece and had 19 cents left-How many were there of them? Ans. 39.

9. A sheep fold was robbed three successive nights; the first night, half the sheep were stolen and half a sheep more; the second, half the remainder and half a sheep more; the last night they took half that were left, and half a sheep more; by this time they were reduced to 12; how many were there at first?

Ans, 103,

10. A can mow an acre of grass in 12 hours, B can muw an acre in 8 hours—how long would it take both of them to mow an acre: H. H.

A. A. As 12 : 72 :: 1 : 6 would be mown by A in 72 hours.

8: 72 :: 1 : 9 would be mown by B in 72 hours.


15 by both of them in 72 hours. A. A. H. H. M. Then as 15 : 1 :: 72 : 4 48 Answer. 11. A gentleman sold a horse for S 80. by which he cleared as much per cent as the horse cost him. I wish to know how much that was ?

Ans. $ 52.47. Rule for such questions. Multiply the price sold for, by 100, add 2500 to the product, and extract the square root of the sum, then deduct 50 from this root for the prime cost.

12. A toper finding a cask of brandy containing one hundred gallons, filled a key therefrom, and refilled the cask with water; coming a second and a third time, he did likewise; after which the owner coming to try the proof, found it half water; query, how much did the toper's keg hold?

Ans. 20.63 gallons. Rule for such questions. Raise the quantity first in the cask to such a power that the index may be one less than the kegs filled from it. Multiply this power by the quantity left in the cask; take such a root of this product as is indicated by the number of kegs fillel, and deduct the root from the quantity first in the cask ; the remainder will be the contents of the keg.

13. How much rye at 60 cents a bushel, must be given in barter for 120 bushels of wheat, at $ 1.00 bushel ?

Ans. 200 bushels. 14. A person having engaged to remove 800 C. a certain distance in 9 days; with 18 horses in 6 days he removed 450 C.-how

many horses will be required to remove the remainder, in the remaining 3 days?

Aps., 28 horses. 15. If a board be 9 inches broad, what length will it require to measure 6 square feet ?

Ans. 8 feet. 16. What money at 58 per cent will clear $ 431.55 în 8 years?

Ans. $ 980.75.


17. A man dying, left $10000 to be divided amongst his. three sons, (whose ages were 19, 16 and 10 years respectively,) in such a manner that their several portions when they became 21 years of age might be equal, reckoning interest at 6 per cent, during their minorities-required the share of each.

$ 2660.235 Ans. 3396.916

3942.849 18. At what times of the day do the hour and minute hands of a watch form a continued straight line?

h. h. m.

h. m.



h. m.

h. m.

h. m.

h. m.

h. m.

Ans. At 6, 7 5,1 8 1011, 9161, 10 214

h. 11 27° 0 3211 1 384 2 4311 3 491 and 4 540 19. If a roll of butter weighs in one scale 4 pounds, and being changed into the other, weighs 61 pounds-what is the true weight?

Ans. 5 pounds. Rule for such questions. Extract the square root of the product of their respective weights. 20. An Eagle is about an inch broad; how


of them laid edge to edge, would reach from New Italy to Harrisburg, a distance of 55 miles?

Ans. 3484800. 21. Admitting the state debt to be $25000000, how long would it take one man to count the money sufficient to pay it in half dollars, allowing him to count 60 per minute, and to be engaged 12 hours each day?

Ans. 1157 da. 4 h. 13 m. 20 sec. 22. The distance from the market house in Harrisburg to the Susquehanna bridge is 200 yards; from thence down the river bank to the Black Horse tavern 497 yards I wish to know the distance upon a straight line from the Black Horse to the market house, admitting it to be a right angled triangle, of which the given distance are the legs.

Ans. 535.73 yds. + 23. Suppose two drovers, A. and B., purchase 100 cattle equally between them for $2400, and divide the cattle in such a way that one of A's and one of B’s are worth $50—I wish to know how many fell to the lot of each, and how much per head they were valued at? Ans. A. 40, valued at $ 30.

B. 60,


« PreviousContinue »