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33. A goldsmith sold a tankard for £10 12s. at 58. 4d. per ounce ; I demand the weight of it.

Ans. 3lb. 3oz. 15pwt.

EXAMPLES FOR PRACTICE.

cts

34. If a staff 5 feet long cast a shade on level ground 7 feet, what is the height of that steeple whose shade at the same time measures 171 feet?

Ans. 122 ft. 35. If į of a ship cost $1960,25, what is the whole worth at that rate?

eighths. $ eighths

As 7 : 1960,25 :: 8: Ans. $2240, 28cts. 51 m. 36. If it take 22 bushels of wheat to make 4 barrels of flour, how many bushels will make 856 barrels ?

Ans. 4708bush. 37. If 12 horses consume 30 bushels of oats in a week, how many bushels will serve 15 horses 3 weeks ?

As 12 : 30 :: 15x3 : Ans. 1121 bushels. 38. Bought of William Merchant 18cwt. 3qrs. of sugar at 8 dollars 12 cents per cwt., and gave him a note on James Paywell for £25 10s. (New England currency ;) the rest I am to pay in cash; how much will make up the deficiency?

Ans. $67, 25cts. 39. Bought 50 pieces of kerseys, each 34 Ells Flemish, at 1 dollar 371 cents per Ell English; what did the whole come to ?

Ans. $1402,50. 40. A merchant bought 250 yards of cambric for 325) dollars ; but finding it damaged, he is willing to loose 25 dollars by the sale of it: what must he demand per Ell English ?

Ans. $1 50c. 2{m. 41. Sold a ship for $2540; I owned fs of her ; what was my part of the money?

Ans. $338,66ş. 42. A merchant bought 18 pipes of wine, and is allowed 6 months credit, but for ready money he gets it 6 cents a gallon cheaper ; how much does he save by paying ready money?

Ans. $136,08. 43. Bought a hogshead of molasses for 13 dollars 75cts. and by accident 9 gallons leaked out; I then sold the remainder at 5 cents a pint ; did I gain or loose, and how much?

Ans. I gained $7,85. 44. Bought 240 yards of cloth at the rate of 71 dollars

for* 5 yards, and sold it again at the rate of 111 dollars for 7 yards ; did I gain or lose in the purchase, and how much?

Ans. I gained $46, 28c. 57.m. + 45. If a man have a salary of 327 English guineas (at 28s.) a year, how much may he spend one day with another, to lay up 625 dollars at the year's end?

Ans. $2, 46c. 81 m. 46. A merchant bought 14 pipes of wine at 14s. 6d., (New York currency,) per gallon ; how many dollars will pay the purchase ?

Ans: $3197,25. 47. A merchant bought 274 Ells Flemish of Holland, at 48 cents per Ell, and sold it again at 94 cents per El English ; how much did he gain on the whole ?

Ans. $23, 1c. 6m. 48. If 50 gallons of water in one hour fall into a cistern which will hold 230 gallons, and by a. pipe in the cistern 35 gallons run out in an hour ; in what time will it be filled ?

Ans. 15h. 20m, 49. A and B depart from the same place and travel the. same road; but A goes 5 days before B at the rate of 20 miles a day; B follows at the rate of 25 miles a day; what distance must B travel to overtake A ? Ans: 500 miles.

RULE OF THREE İNVERSE. i. The Rule of Three Inverse teaches, from three given numbers to find a fourth, which shall have the same propora tion to the second, as the first has to the third.

2. When more requires more, or less requires less, the question belongs to the Rule of Three Direct.

3. But if more requires less, or less requires more, the question belongs to the Rule of Three Inverse.

[More requiring more is when the third term is greater than the first, and requires the fourth term to be greater than the second; less requiring less is when the third term is less than the first, and requires the fourth term to be less than the second. Also, more requiring less is when the third term is greater than the first, and requires the fourth term to be less than the second ; and less requiring more is

when the third term is less than the first, and requires the fourth term to be greater than the second.]

Thus, if 3.men can perform a piece of work in 6 days, how long will it take 6 men to do the same? It is evident that if three men require 6 days, 6 men will do it in half the number of days, that is, 3 days Here more requires less, viz. : the more men the less time is required.

If 6 men require 3 days, how many days will 3 men require ? Ans. It is evident that 3 men will require as much again time as 6 men would, viz. : 6 days. Here less rea quires more, that is, the less the number of men is, the more days are required.

RULE.

1. State the question, and reduce tné terms the same as in the Rule of Three Direct.

2. Multiply the first and second terms together, and divide the product by the third, the quotient will be the answer in the same denomination that the middle term was reduced to.

EXAMPLES.

a square foot ?

1. If 10 men can dig a ditch in 18 days, how many men will do the same in 6 days?

Ans. 30 men. 2. If a man perform a journey in 10 days, when the days are 12 hours long, in how many days will he perform the same when the days are but 10 hours long ? Ans. 12 days.

3. If 20 bushels of grain, at 75 cents a bushel, will pay a debt, how many bushels, at 50 cents a bushel, will pay the same?

Ans. 30 bushels. 4. What length of board that is 5] inches wide will make

Ans. 27 inches. 5. If when wheat is $1,25 per bushel the penny-loaf will weigh 9oz., what ought it to weigh when wheat is $1,00 per bushel ?

Ans. 11oz. 5pwt. 6. If $100 in 12 months gain $6 interest, what principal will gain the same in 8 months ?

Ans. $150. 7. If 5 dollars will pay for the carriage of 3cwt. 150 miles, how far may 15cwt. be carried for the same money?

Ans 30 miles.

8. How many men must be employed to finish in 8 days what 18 men would do in 24 days ?

Ans. 54 men. 9. There was a certain building erected in 8 months by 120 workmen, but the same being demolished, it is required to be rebuilt in 2 months ; I demand how many men must be employed to do it?

Ans. 480 men. 10. Suppose 850 soldiers are placed in a garrison, and their provisions calculated to last but 2 months; how many must leave the garrison, that the same provisions may last those who remain, 5 months ?

Ans. 510. 11. How many yards of cambric, yard wide, will line 5) yards of cloth which is 13 yards wide ?

Ans. 9 yards Oqrs. 2 nails. 12. A regiment of soldiers, consisting of 652 men, is to be clothed, each suit to contain 3 yards of cloth which is 11 yards wide, and lined with flannel i yard wide; how many yards of flannel will line the whole"?

Ans. 5324yds. 2qrs. 2 nails.

Note. The foregoing are the common methods of solving questions in the Ruie of Three Direct and Inverse, which we consider most applicable to general prac tice.- There is, however, another method of solving questions in these Rules, without making any distinction between Direct and Inverse proportion, and as some may have a preference for this mothod of operation, we therefore insert the following Rule, in which no distinction is made between Direct and Inverse proportion, together with some examples.

RULE.

Write that number for the 3d term which is of the same name or kind with the answer; then, if by the nature of the question the answer ought to be greater than the third term, write the greater of the two remaining numbers for the second term, and the less number for the first term. But if the answer ought to be less than the third term, place the least of the two remaining numbers for the second term, and the greater for the first term; then multiply the second and. third terms together, and divide the product by the first term, and the quotient will be the answer in the same name of the third term.

EXAMPLES.

dols.

dols.

dols.

men.

1. If 6 yards cost $10, 2. If $20 will buy 12yds., what will 12 yards cost? how

many yards will 10dols.

buy? yds. yds.

yds. Thus, as 6 : 12 :: 10 :

20 :10 :: 12 : Ans. 20 dollars.

Ans. 6 yards. 3. If 8 men can build a wall in 20 days, how many men will do the same in 5 days ?

days. days.

As 5 : 20 ::8: Ans. 32 men. 4. If 32 men can build a wall in 5 days, how many men will do the same in 20 days ?

days. days. mon.

As 20: 5 :: 32 : Ans. 8 men. 5. If 8 bushels of wheat cost 11 dollars, what will 25 bushels cost ? bush. bush. dols.

As 8 : 25 :: 11 :

11 3)275

Ans. $343 6. If a man perform a journey in 11 days when the days are 15 hours long, in how many days will he perform the same when the days are but 10 hours long?

hours. hours. days. As 10 : 15 :: 11 :

11 10)165

Answer 16 days. 7. How many yards of cloth which is 3 yard wide will line 9 yards of broadcloth, which is 14 yards wide ?

yds.

As 3 : 11 :: 9 : Ans. 15 yards. Note. When the first and second terms are of different denominations, they must both be reduced to the same denomination. And if the third term be a compound number, reduce it to the lowest name mentioned.

8. If 3cwt. lqr. of sugar cost $21, 6cts., what cost 35 cwt. ?

qrs. qrs.

cts. As 13 : 140 :: 2106 : Ans. $226,80.

qrs. yds.

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