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22. A. and B., traded in company. A.'s money, which was $9621.75, remained in the firm 11.8mo. How long was B.'s money, which was $12770.00, in the firm, the gain being divided equally?

23. A. B. & C. invested $16329.00 in merchandise. They sold their goods so as to gain $4101.375. How much of the gain ought B. to receive, he having contributed $7075.15?

24. A tailor made 37 coats, each coat containing 1.87yd. of cloth, 1.5 yards wide. How much silk that is .67 yards wide, will be required to line the whole?

25. When a pole 4 ft. high, casts a shadow of 4.25 feet, what is the height of a steeple, that casts a shadow of 197 feet?

26. How much sugar can I buy for $96.25, if I pay $71.50 for 9cwt. 2qr 271b.?

27. If 2 lb. of indigo cost $4.625, what will be the cost of 9lb.?

EXAMPLE FOR THE BOARD.

If 12 men can build a wall 16 feet long, 2 feet thick, and 4 feet high, in a week, how many men can build a wall 24 feet long, 3 feet thick, and 6 feet high, in the same time?

16 long,: 24 long,
2 thick, : 4 thick,
4 high, :
6 high,

128

: 576

:: 12 men, : men.

:: 12 men,: 54 men. Ans.

This is a question in COMPOUND PROPORTION. The third term is determined in the same way as in Simple Proportion. Of the remaining numbers, we compare any two of a kind, writing one for a first term, and the other for a second, until all are brought down. Then, the product of the first terms, : the product of the second terms,:: the third term, the Answer.

28. If the wages of 24 men for 3.5 days are $96.50, what will be the wages of 19 men for 7.75 days?

29. If 18 men can build a wall 100 ft. long 2ft. wide, and 6ft. high, in a given time, how much wall that is 3ft. wide and 9ft. high, can 21 men build in the same time?

30. If 7 men can reap 115.5 acres of wheat in 8.25 days, how many men can reap 276.3 acres in 7.675 days?

31. If the interest of $231.00 for lyr. 5mo. is $20.95, what will be the interest of $500.00 for 3yr. 11mo. at the same rate?

32. If 16 horses eat 96 bushels of oats in 2mo., how many horses will eat 153 bushels in 1 month? 33. If I pay 17 men $204.00 for 8 days' work, how many men can I hire 19.5 days, for $380.25?

34. If 46.9 acres will pasture 29 oxen 11 weeks, how many acres will pasture 17 oxen 21.7 weeks?

35. My horse can travel 169 miles in 3 days, when the days are 10 hours long. In how many days of 8.75 hours will he travel 243.7 miles?

36. If I pay $15.00 for the cartage of 9 tons of coal 35 miles, how much must I pay for carting 13 tons 8 miles?

37. If 18 men will work 7 days for $133.75, how many days will 13 men work for $94.00?

38. If 12 sacks of sugar, at 7 cents a pound, cost $83.61, what must I give for 16 sacks, at 8 cents a pound?

39. How many men will be required to perform a piece of work in 7 days, working 9 hours a day, that 25 men can perform in 12 days, by working 8 hours a day?

40. A vessel has provisions sufficient to furnish 30 men for 6 months, allowing each man 18 ounces.a day. How long would the same provisions furnish 45 men, allowing 14 ounces per day?

REVIEW.

Give an example of a Compound Number. Repeat the tables of Compound Numbers. Give an example in Compound Addition; and tell how the sum may be obtained. Give an example in Compound Subtraction; and tell how you obtain the difference. Give an example in Compound Multiplication; and tell how you obtain the product. Give an example in Compound Division; and tell how you obtain the quotient. How do you obtain the Square Contents of any surface? How do you obtain the Cubical, or Solid Contents of any regular body? What do you understand by Per Centage? What is the Rate per cent.? What is Interest? What is the Principal?-the Rate? -the Amount? Knowing the rate for one year, how do we obtain the rate for any given time? Having found the rate for the time, how is the interest found? When the rate is 6 per cent. how is the rate for any given time found? What is the present worth of any sum of money? How is it found? What is the Discount; and how is it found? How are Fractions obtained? Is the Divisor or the Dividend, written for the Numerator? What is a proper Fraction? an improper Fraction?-a mixed Number?-a Compound Fraction? How may an improper Fraction be reduced to a whole or mixed Number? How may a mixed Number be reduced to an improper Fraction? How may a whole Number be written in the form of an improper Fraction? How may a Compound Fraction be reduced to a simple one? How may a Fraction be reduced to a Decimal? How do you add Fractions? How do you reduce Fractions to a common Denominator? How do you subtract Fractions? What if the fraction in the subtrahend is larger than that in the minuend? How do you multiply Fractions together? What two methods are given for dividing Fractions? How do you reduce Fractions to their lowest terms? How do you reduce Decimals to Fractions? How do you reduce Fractions of a higher denomination to whole Numbers of a lower? How do you reduce whole Numbers of a lower denomination to the Fraction of a higher?

What do you understand by the Ratio of two numbers? What is the ratio of 6 to 11? 16 to 15? 29 to 31? How is a ratio usually expressed? How is it read? How may two equal ratios be written together, and read? What is such an expression called? What is the first term of every ratio called? The second term? May the position of the antecedents and consequents be changed? What are the extremes of a proportion? The means? How can you show that the product of the extremes is equal to the product of the means? When one extreme and the two means are given, how do you find the other extreme? Propose a sum in Proportion; and work it on the board. How are the numbers arranged in Compound Proportion?

MISCELLANEOUS EXAMPLES.

1. A merchant bought flour for $1650.22, wheat for $843.77, barley for $905.17, rye for $1017.63, and oats for $741.625. How much did he gain, by selling the whole for $5331.00?

2. A locomotive travelled at the rate of 14.9 miles per hour, for 2.33 hours, and 16.08 miles per hour for 3.15 hours. What distance did it go in the whole time?

3. A grain dealer has 145 sacks of wheat, containing 2.45 bushels each, 170 sacks containing 3.09 bushels each, and 2181 sacks, containing 3.7 bushels each. He sells 4906.85 bushels; and wishes to divide the remainder equally between 4 bins. How much must he put into each bin?

4. If I purchase 128gal. 2qt. of molasses from each of 9 men, and put the whole in 13 casks, how much must each cask hold ?

5. A clerk's salary is $1025.00 a year, and his expenses $2.25 a day. How much will he save in 4.63 years?

6. If 259gal. 2qt. of molasses cost $18.75, what is the price of a pint?

7. An apothecary had 63 bottles of equal size, the whole containing 7 Cong. 30. 15f3. How much did each hold; and how many drops of water would fill the whole?

8. Divide .0000760093 by 100119.7.

9. How many seconds will there have been from the commencement of the Christian era till the close of the year 1844?

10. What number divided by 306800000 will give 496.38?

11. Add 17, of of of 16, 39 and, and subtract 2 from the sum.

12. Reduce of a furlong to rods, &c., and subtract it from 2 miles.

13. The president, cashier, and teller of a bank, receive together $4097.00. Of this amount the president receives, the cashier of the remainder, and the teller the rest. How much does each receive?

14. A grocer bought 189gal. 2qt. of molasses for $63.50. At what rate must he sell it per gallon, in order to gain 10 per cent.?

15. A. borrowed of B. $1197.63, for which he gave his note, dated Aug. 1, 1833. How much was due on the note May 21, 1841, computing interest at 6 per cent.?

16. What is the difference between the interest and the discount of $2009.00 for 4yr. 6mo. 24dy.; interest at 6 per cent.?

17. At what time, between 8 and 9 o'clock, are the hour and minute hands of a watch exactly together?

18. How many bricks, 8 inches long, 4 inches wide, and 2 inches thick, are in a pile 9ft. long, 4 feet wide, and 6 feet high?

19. How many feet from Boston to Washington, calling the distance 435m. 7fur. 38r.? How long would it take to walk between the two places, taking 2 steps in a second, and 2.55 feet at each step ?

20. What number, multiplied by 51⁄2, will give 314?

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