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13. If 476 be the square root of a number, what will be the quotient of that number divided by half its root ?

Ans. 952. 14. From of a league take of a mile.

Ans. 2 mi. 5 rods, 113 feet. 15. There are two numbers the greater of which is 30 times 80, and their difference is 12 times 25; what is their sum ?

Ans. 4500. 16. What number is that which multiplied by the 47th part of 23500 will produce 400000 ?

Ans. 800. 17. Reduce of 1 of 4 hours, to the fraction of a day.

Ans. I. 18. Suppose a mast is erected so that g of its length is in the ground, 12 feet of it in the water, and & of its length above the water; what is the whole length of the mast?

Ans. 216 feet. 19. If 20 bushels of wheat at $1.35 a bushel be mixed with 10 bushels of rye at 90 cents a bushel ; what will a bushel of the mixture be worth ?

Ans. 1.20. 20. What is the sum of į of a ton, and 15 of a hundred weight?

Ans. 8 cwt. 1 21 lbs. 21. What will 9 cwt. of cheese cost at 1 £. 11 s. 5 d. per

Ans. 14 £. 2 s. 9 d. 22. If 30 dollars be divided equally among 27 men, how much will each man receive ?

Ans. 1.111. 23. What is the value of .857 of a day?

Ans. 20 h. 34 m, 4 sec. 24. What is the difference between 400 years and 98 years, 3 mo. 8 h. 10 sec. ?

Ans. 301 yrs. 8 mo. 3 wks. 6 ds. 15 h. 59 m. 50 sec. 25. A man being asked his age answered that if its 1 and } were added to it, the sum would be 77; what was his

Ans. 42 years. 26. How much in length, that is 44 inches broad, will make a square foot ?

Ans. 32 inches. 27. What will 7211 yards of cloth cost at 1 s. 3d. per yard ?

Ans. 450 £, 13 s. 9 d. 28. What will 2184 bushels of beans come to at 12 s. 6 d.

Ans. 136 £. 11 s. 3 d. 29. What is the value of 136 £. 11 s. 3 d. in Federal mo

Ans. 455.21.

qr.

cwt. ?

age ?

per bushel ?

ney ?

QUESTION.-What is the first thing to be done in obtaining an answer to sumn 25th

30. If iron cost $6.50 per cwt. ; what is it per pound?

Ans. 0.058. 31. If # of g of } of a ship be worth $ of of 1 of the cargo valued at 40000 dollars; what is the value of the ship and cargo?

Ans. 50744.81. 32. Reduce to a decimal fraction.

Ans. .8. 33. A and B gained 1260 dollars, of which A is to have ten per cent more than B; what is the share of each?

A's 660 dollars.

Ans. { B's 600

do.

34. A general has an army of 103041 men, and wishes to form them into a square; how many must he place in rank and file?

Ans. 321. 35. What is the quotient of 8 divided by 12?

Ans. 3. 36. What will a board measure, which is 18 feet long and 1 foot 2 inches wide ?

Ans. 21 feet. 37. Two men depart from the same place, one goes north, the other south. One travels at the rate of 25 miles per day-the other at the rate of 32 miles per day; how far are they from each other 5 days after their departure ?

Ans. 285 miles. 38. What part of 25 is of one?

39. A can do a piece of work in 10 days, and B in 13; in what time will both together finish it? Ans. 515. days.

40. What is the square root of 106929? Ans. 327.

Aps. 5.

SECTION II.

1. A person having spent 10 dollars more than f of his yearly income, had 15 dollars more than 1 of it left; what was his income?

Ans. 150 dollars. 2. Let 5205} be divided by of 91. Ans. 711.

3. What is the least number which can be divided by the nine digits separately without a remainder ? Ans. 2520. 4. What is the square root of 196 ?

Ans. 14. 5. A young man received 210 dollars, which was equal to of his elder brother's portion, and three times the elder

QUESTIONS.—How do you reason on the 39th sum?

How will you prove that 327 is the true answer to the 40th sum ?

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yard ?

acre ?

brother's portion was equal to the father's estate; what was the estate.

Ans. 1890 dolls. 6. The population in the several New England States in 1830, was as follows: Maine 399462; New Hampshire 269533 ; Vermont 280679; Massachusetts 610014; Rhode Island 97210; Connecticut 297711; what was the whole population of New England at that time?

Ans. 1954609. 7. What is the cube root of 389017?

Ans. 73. 8. What is the cube root of $?

Ans. .703. 9. Divide 2345678964 by 6.

Ans. 390946494. 10. What cost 846 yards of broadcloth at 18 s. 6 d. per

Ans. 782 £. 11 s. 11. If a gallon of wine cost 6 s. 8 d. and is sold for 7 s. 2 d.; what is gained per cent ? Ans. 74 per cent. 12. Reduce 3 roods and 24 rods to the decimal of an

Ans. .9. 13. What decimal is equivalent to ? Ans. .375. 14. Reduce 3} bushels to the decimal of a quarter ?

Ans. .416. 15. What is the interest of 325.41 dollars for 3

years

and 4 months at 5 per cent. ?

Ans. 54.235. 16. A note for 730 dollars and interest at 6 per cent. was paid 5 years, 7 months, 12 days, after date; what was the amount at the time of payment ?

Ans. 975.99. 17. From 100046 take 10009.

Ans. 90037. 18. What is the square root of 11.99998881 ?

Ans. 3.4641. 19. What number multiplied into itself will produce 42).

Ans. 63. 20. What number multiplied into itself will produce 123201 ?

Ans. 351. 21. If 37 £. 16 s. be divided equally among 24

men,

how much will each man receive ?

Ans. 1 £. 11 s. 6 d. 22. How many tons are there in 6881280 drachms?

Ans. 12. 23. In 244 bushels, how many quarts? Ans. 784.

24. What will 25 bushels of corn cost at 92 cents per bushel ?

Ans. 23 dolls.

QUESTIONS.—What is the first step in solving the 8th example ? After having reduced the fraction to a decimal, what is next to be done ?

25. A person having of a vessel, sold if of his share for 570 dollars; what was the whole vessel worth at this rate.

Ans. 1266.666. 26. A person having spent 1 and f of his money, had $180 left; what had he at first?

Ans. 1080 dolls. 27. What number is that which being increased by its ; and its 4 and 15 more, will be trebled ?

Ans. 20. 28. If the shadow of a staff 4 feet long, at a given hour is 7 feet long; what is the length of a steeple whose shadow at the same hour is 198 feet?

Ans. 1137. 29. If a man travel 120 miles in 6 days, when the days are 12 hours long; how many days of 16 hours long will he require to travel 2880 miles ?

Ans. 108 days. 30. Two ships sailed from the same port; one sailed due north 60 leagues in 2 days—the other sailed due east 45 leagues in the same time; how far were they apart at the end of the second day?

Ans. 75 leagues. 31. Divide 1673652552 by 4092. Ans. 409006. 32. Multiply 5032 by 304.

Ans. 1529728. 33. Multiply 2486 by 1000.

Ans. 2486000. 34. Divide 50 by 1 of one.

Ans. 100. 35. Bought 150 yards of cloth for 45 £.; for how much must it be sold to gain 25 per cent. ? Ans. 56 £. 5 s.

36. A has 200 yards of broadcloth, worth $2.50 per yard, for which B gives him $250 in cash, and 500 gallons of molasses; at what does B value his molasses per gallon?

Ans. 50 cents. 37. Multiply .25 by .25.

Ans. .0625. 38. Divide 56 by $.112.

Ans. .5. 39. What will 140 reams of paper cost, at $2.35 per ream?

Ans. $329. 40. Divide 145260 by 108.

Ans. 1345.

QUESTIONS.--What method of reasoning do you pursue in solving the 29th example?

How do you obtain the answer to the 30th sum? Why do you square 60 and 45 leagues, and then extract the square root of the sum of these two squares, in order to come to the true result?

What general principle is involved in this process, which is true of all right angled triangles ?

How can you prove that the quotient in Ex. 34, should be greater than the dividend ?

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SECTION III,

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1. What will 35 lbs. 8 oz. of cheese cost, at 8 cents per pound?

Ans. $2.84. 2. A privateer of 65 men took a prize, which, being equally divided among them, gave to each man 119 dollars; what was the value of the prize?

Ans. 7735 dolls. 3. What will 9 tons of hay come to at 14 dollars per ton?

Ans. 136-1 dolls. 4. The war between England and the United States commenced April 19th, 1775, and peace took place January 20th, 1783; how long did the war continue ?

Ans. 7 yrs. 9 mo. 1 day. 5. What is the difference between .999 and 1 ?

Ans. .001. 6. Divide 60000 by 100.

Ans. 600. 7. Divide 34.72 by 1.24.

Ans. 28. 8. Reduce minutes to the decimal of a day.

Ans. .009722, &c. 9. What is the value of .625 shil. ?

Ans. 77 d. 10. If of a yard of velvet cost of a pound, what will It of a yard cost ?

Ans. 6 s. 8 d. 11. What part of a pound is one penny?

Ans. 2o. 12. What will 2 cords of wood amount to, if 4 off of of a cord cost of % of a dollar ?

Ans. $12. 13. What sum, at interest for 2 years at 41 per cent., will amount to $272,50 ?

Ans. $250. 14. At what rate per cent. will 300 dollars amount to 396 dollars in 8 years ?

Ans. 4 per cent. 15. Reduce 118 lbs. 1 oz. 6 pwts. 10 grs. to grains.

Ans. 680314 grs. 16. What will be the expense of keeping 20 horses for a year, at 16 cents per day for each ?

Ans. $1168. 17. A drover agreed for 1 dozen lambs at the rate of 1 cent for the first, 2 cents for the second, 4 cents for the third, and so on, doubling the price at every lamb; what was the price of the last ?

Ans. $20.48. 18. The population of Sweden in 1826 was 2751582, that of Norway 1050132; how many more people in Sweden than in Norway?

Ans. 1701450. QUESTION.-What method of reasoning do you pursue in solving the 18th example ?

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