Imágenes de páginas
PDF
EPUB

10. If a piece of linen, containing 20 yards, cost 27. 10s., what would 155 yards cost at the same rate?

Ans. 197. 7s. 6d. 11. If the yearly rent of a farm containing 182 acres be $273, what is the rent of a part of it containing 43 acres? As 182 A.: 43 A. :: $273 : $64.50 Ans. 12. How many barrels of flour can I purchase for $744 when the price of flour is $6 per barrel?

As $6 $744: 1 bar. : 124 barrels, Ans. 13. If1cwt. of beef cost $5.25, what will 39 cwt. cost? Ans. $204.75

14. If 25 men can do a certain piece of work in 60 days, how many men would do the same in 100 days?

As 100 da.: 60 da. :: 25 men: 15 men, Ans. Here, because it would not require as many men to do the work in 100 days as it would to do it in 60 days, I make the less number of days the second term, and the greater the first term.

15. If 6 men can build a certain wall in 192 days, how many men must be employed to build it in 24 days?

Ans. 48. 16. If the shilling loaf weighs 36 ounces when flour is $4 per barrel, how much must it weigh when flour is $6 per barrel?

As $6 $4: 36 oz.: 24 oz, Ans.

:

It is evident that the higher the price of flour is, the lighter the shilling loaf must be; and, because the answer must be less than the third term, I make the less remaining number the second term, and the greater the first.

17. If 84 sheep can be grazed in a certain field for 12 days, how long may 112 sheep be grazed equally well in the same field? Ans. 9 days. 18. If a person lend me $270 for 8 months; in return for his kindness, how much money ought I to lend him for 18 months? Ans. $120. 19. Suppose a principal of $360 to produce a certain interest in 5 months; in what time, at the same rate, will $150 produce the same interest? Ans. 12 months.

20. If $100 principal gain $6 interest in a year, how much will $49 gain in the same time, at that rate?

Prin. prin. int. int.

As $100: $49 :: $6: $2.94, Ans.

Here all the terms are money. The $6 interest is made the third term because the answer is interest; and the less principal is made the second term and the greater the first, according to the Rule.

21. If I sell goods to the amount of $400, and thereby gain $75.50, how much should I gain, at the same rate, by selling goods to the amount of $1000? Ans. $188.75 22. If a staff 4 feet high cast a shade on level ground 6 feet, what is the height of a tower whose shadow at the same time extends 100 feet?

Shade. shade. height. height.

As 6 ft. 100 ft. :: 4 ft.: 66 ft. 8 in. Ans. In each of the fourteen questions next following, (viz. questions 23d to 36th,) the first and second terms are of different denominations.

23. If 1 lb. of butter cost 1 s. 5 d., what would 8 lb. 6 oz. cost?

lb.

S. d.

lb. oz.

[blocks in formation]

1..5:

[blocks in formation]

67

64

38

32

Rem. 6 d.
4

Here, 1 reduce the first and second terms to ounces, to make them both simple numbers of the same denomination: I also reduce the third term to the lowest denomination of which it consists.

I then multiply the second and third terms together, and divide their product by the first term; and the quotient is 142 pence; 16)24(1q. which I reduce to shillings, and have 11s. 10d. for the answer.

16

[blocks in formation]

N. B. The learner ought to bear in mind, that the first and second terms must not only be reduced to simple numbers when they are compound numbers, but they must always be simple numbers of the same name, or denomination.

24. If 1 lb. of tobacco cost 1s. 2d. what will 5lb. 14 oz. cost? Ans. 6s. 104 d. 25. What is the value of 5 acres, 2 roods, of land, if one acre be worth 127. 17s.?

As 1A. 5 A. 2R. :: 127. 17s. the 4th term.
S. d. L. S. d.

R. R.

S.

Or, as 4: 22 :: 257: 1413 .. 6=70 .. 13..6 Ans. 26. If the rent of 5 acres of land be 41. 13s. 4 d. how much land could be rented, at the same rate, for 70l. 10s. 6d.? L. S. d. L. S. d. A.

As 4.. 13.4 : 70 .. 10 .. 6:5: the 4th term.

[blocks in formation]
[ocr errors]

10 Ans.

Or, as 1120: 16926 :: 5 : 75..2 27. If 12 bushels of wheat cost 67. 10s. 8d. how many bushels may be bought for 117. 8s. 8d.? Ans. 21 bush. 28. How much will 250 bushels, 1 peck, of salt cost, at 52 cents per bushel ?

As 1 bush.: 250bush. 1 pk. :: $.52: the 4th term.

Or, as 4 pks.: 1001 pk. :: $.52 : $130.13, Ans. 29. An eagle contains 11 pwt. 6 gr. of standard gold.* What is the value of 1 lb. of gold, at that rate?

As 11 pwt. 6 gr.: 1lb. :: $10: the 4th term.

Or, as 270 gr.: 5760 gr. :: $10 : $2133 Ans. 30. An American silver dollar contains 17 pwt. 8gr. of standard silver.† What is the value of 1 lb. of silver, at that rate? Ans. $13. 31. If the weight of an eagle be 11 pwt. 6 gr. Troy, and 175 oz. Troy be equal to 192 oz. Avoirdupois, what is the Avoirdupois weight of an eagle?

Troy wt. Troy wt.

Avoir. wt.

As 175 oz. 11 pwt. 6 gr. :: 192 oz.: the 4th term. Or, as 84000 gr.: 270 gr. :: 192 oz.: 913 drams, Ans.

*The weight of an eagle is 11 pwt. 6 gr; but the quantity of pure gold in an eagle is only 10 pwt. 7 1-2 gr., the rest being alloy.

+ An American dollar contains 15 pwt. 11 1-4 gr. of pure silver, and 1 pwt 20 3-4 gr. of alloy.

32. An American silver dollar weighs 17 pwt. 8 gr. Troy: required the Avoirdupois weight? Ans. 15 drams. 33. If 7 tons of potashes cost $262.50, what would 9 cwt. 3qr. cost? Ans. $18.281+

34. How much must be paid for 8cwt. 3qr. 25lb. of pigiron, at the rate of $28 per ton? Ans. $12.5625 35. If the digging of a mile of canal cost $6500, what will the digging of 30 miles, 7 furlongs, 21 rods, cost? Ans. $201114.0625 36. If a person walk 17 miles in 5 hours, 12 min. 31 sec., how far would he walk, at the same rate, in 3 hours, 40 min. 36 sec.? Ans. 12 miles.

In each of the eleven questions next following, (viz. questions 37th to 47th,) there are decimals in one or both of the terms in the first and second places.

37. If a piece of cloth containing 25.5 yards be worth $12.75, what is the value of 3 yards of it? Ans, $1.50 38. If 1.47 cwt. of sugar be worth $20, what is 1.7 cwt. worth? Ans. $23.129+

39. If 9.75 bushels of wheat cost $15, what would .5 of a bushel cost? Ans. 76 c. 9m.+ 40. If a man lays out $121.25 in merchandize, and thereby gains $37.50, how much would he gain, at the same rate, by laying out $500 ?

As $121.25 laid out: $500 laid out :: $37.50 gained : $154.639+gained, Ans.

Note 3.-When the third term is a compound quantity, (i. e. when it consists of several denominations,) and there are decimal figures in the first and second terms, or in either of them; if you do not wish to reduce the third term to a simple quantity, you may equalize the decimal places in the first and second terms, when they are unequal, by annexing to the term which has the fewest decimal places, as many ciphers as may be necessary to make up as many places of decimals as there are in the other term; and then reject the decimal points from both these terms, and consider them as whole numbers. Then multiply the third term by the second, and divide the product by the first, (by Compound Multiplication and Division,) and the quotient

will be the answer. * This method may also be used when the third term is not a compound quantity, when it is more convenient than the common mode. By proceeding in this way, decimal fractions, which would sometimes be very troublesome, may be avoided in the operation.-It will be proper for the learner to solve questions 41st to 47th in this way.

41. If 12lb. 2oz. of butter cost $2, how much butter may be bought for $1.20?

As $2 $1.20 :: 12lb. 2oz.: the 4th term.

:

By annexing two ciphers to the first term, and rejecting the decimal point from the second, (which is in effect the same as reducing the first and second terms to cents,) the statement is as follows:

As 200 120 :: 12lb. 2oz.: 7lb. 4 oz. Ans. 42. If 1.2 bushels of wheat cost 7s. 6d. what would 2.75 bushels cost?

As 1.2 bush. : 2.75 bush. :: 7s. 6d. : the 4th term. Or, as 120 275 :: 7s. 6d. : 17s. 24d. Ans. 43. If 2.75 yards of cloth cost 4l. 13s. 6d. what cost 12.25 yards? Ans. 201. 16s. 6d. 44. If the rent of 7 acres and 1 rood of land be $12.75, how much land could be rented for $100?

Ans. 56A. 3R. 18sq. rd.+ 45. If 25.75 bushels of rye cost 10l. what would 4.5 bushels cost?

As 25.75 bush. : 4.5 bush. :: 107.: the 4th term. Or, as 2575: 450 :: 107. : 17. 14s. 114d.† Ans. The same answer may be obtained without rejecting the decimal points from the first and second terms, viz. as follows:

As 25.75 bush. : 4.5 bush. :: 107.

10

L.

25.75)45.0(1.7475+ Then, by reducing the decimal of a pound to shillings, &c., by Case II. Reduc

*It is evident that by equalizing the decimal places in the multiplier and divisor, (i.e. in the first and second terms,)and then rejecting the decimal points, both numbers are increased in the same ratio; and hence the answer must evidently be the same as though the decimal points were retained, as usual.

« AnteriorContinuar »