Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

EXAMPLES.

1 A merchant has 40lb. of tea, at 6s. per lb. which he would mix with some at 5s 8d. at 5s 2d. and at 4s 6d. per lb. how much of each sort must he take, to mix with the 40lb. that he may sell the mixture at 5s 5d. per lb.

65

54

62

[merged small][merged small][ocr errors]

given.
As 14: $.0 :
240:

}

3+7=10

3+7=10

11+3=14

11+3=14 against the price of the quantity

[blocks in formation]

per

[ocr errors]

2 How much barley at 2s 6d. rye at 3s. and wheat at 4s. per bushel, must be mixed with 12 bushels of oats at 18d. per bushel, that the whole may rate at 1s 10d. per bushel? answer 1 bushel of each. 3 How much gold of 16, 20, and 24 carats fine, and how much alloy, must be mixed with 10oz. of 18 carats fine, that the composition may be 22 carats fine?

answer 100%. of 16 carats fine, 10 of 20, 170 of 24, and 10 of alloy.

4 Ten bushels of wheat at 4s. per bushel, with rye at 3s. barley at 2s. and oats at 1s. what quantity of these must be mixed with the wheat to rate at 2s 4d. per bushel ?

2bu. 2p. of rye,

1 ans.

5

barley,

2 ans.

40bu. of rye,
50 barley,

[blocks in formation]

When the rates of the several simples, the quantity to be compounded, and the mean rate thereof are given, to find the quantity of each simple;

RULE.

RULE.

Link the several prices, and place their differences as before; then,

As the sum of the differences

Is to the quantity to be compounded;
So is the difference opposite each rate
To the required quantity of that price.

EXAMPLES.

1 A brewer had 3 sorts of beer, viz. at 10d. 8d. and 6d. per gallon; how much of each sort must he take, to make 30 gallons, worth 7d. per gallon?

[ocr errors]

1 As 6:30: 1 to 5 gals. at 10d. & 8d. 6:30: 4 to 20

at 6d.

answer.

[blocks in formation]

1

[blocks in formation]

2 A druggist compounds medicines, at 4s. 5s. and 8s. per lb. to make two parcels, one of 21lb, at 6s. the other of 35lb. at 7s. per lb. what quantity of each must be taken?

answer

L6lb. at 4s.

9

5

8

=21lb. at 6s. &c.

}

5lb. at 4s..

5

25

5

8

= 35lb. at 7s. per lb.

3 A merchant had 4 sorts of coffee, at 8d. 12d. 18d. and 22d. per lb. the worst would not sell, and the best was too dear, he therefore concluded to mix 120 lb. what quantity of each must he take, so as to sell at 16d. per lb.

answer 36lb. at 8d. 12 at 12d. 24 at 18d. and 48 at 22d. 4 How many gallons of water must be mixed with wine át 4s. per gallon, so as to fill a vessel of 80 gallons, that may be afforded at 2s 9d. per gallon?

answer 25 gallons of water with 55 of wine. 5 A goldsmith has gold of 15, 17, 20, and 22 carats fine, and would melt together of each of these so much, as to make a mass of 400z. of 18 carats fine; how much of each sort is necessary ?

answer 16oz. of 15, 4 of 17, 8 of 20, & 12 of 22 carats fine.

POSITION.

POSITION.

OSITION is a rule for finding an unknown number, by one or more supposed numbers; and is either single or double.

SINGLE POSITION.

Single position teaches to resolve such questions as require only one supposed number.

RULE.

Work with a supposed number according to the tenor of the question; then,

As the result of that operation

Is to the supposed number;
So is the number given

To that required.

PROOF.

Work with the answer according to the tenor of the question, and the result must equal the given number.

Note. If the results of two or more supposed numbers be in the same proportion as the number supposed : or,

If upon working with two supposed numbers, and multiplying each of them by the result of the other, the products be equal, then the question may be solved by single position, otherwise not.

EXAMPLES.

1 A person, after spending and of his money, had 601. left; what had he at first ?

£. £ £ £ £•

Suppose 24 As 10: 24: 60: 144 answer.

[ocr errors][merged small][merged small][merged small][merged small][merged small][merged small]

2 B's age is 1 A's; C's twice B's; both with A's make

132 years; how old is each of them?

answer A 24, B 36, and C 72 years.

3 What sum is that, of which the , and make 74. answer 1201. 4. What sum of money, at 6 per cent. per annum, simple interest, will amount to 500l. in 10 years? answer 312l 10s.

5 Three unequal vents will severally empty a vessel of 120 gallons in 1 hour, 2 hours, and 3 hours; if running together, what time is necessary P. answer 33min. 437 sec. 6 Of a certain sum given A, B1, B2, and D the rest, which is 281. the sum is required?

answer 1121. 7. What is the age of a person who says, that if % of the years I have lived be multiplied by 7, and 3 of them be added to the product, the sum will be 292? answer 60 years. 8 Required the sum, the 4, 4, and of which made 941.

answer 1201. 9 What sum, at 6 per cent. per annum, will amount to 8601. in 12 years?

answer 5007.

10 A person having about him a certain number of dollars, said, that 1, 1, and 1 of them would make 57; how many had he?

answer 60.

11. A schoolmaster being asked how many scholars he had, answered, if to double the number I add 4, 4, and 4 of them, I shall have 333; how many had he? answer 108

12 A saves of his income; but B who has the same salary, by living twice as fast as A, sinks 50l. a year; how much then have they per annum? answer 150l. each. 13 The yearly interest of Charlotte's money, at 6 cent. exceeds of the principal by an 1007. and she does not intend to marry any man, who is not scholar enough to tell her fortune; pray what is it ? answer 100001.

DOUBLE POSITION.

per

Double position teaches to solve such questions as require two supposed numbers in the operation.

RULE.

Suppose two numbers, and work with each agreeably to the tenor of the question, noting the errors of the results: multiply the errors of each operation into the supposed number of the other; then,

If the errors be alike, i. e. both too much, or too little, take their difference for a divisor, and the difference of the product for a dividend: but if unlike, take their sum for a divisor, and the sum of the products for a dividend.

Note. In many instances, if 0 be used for the first, and for the second of the supposed number, the first of the errors, divided by their difference, will be the answer.

Proof as in single position.

EXAMPLES.

1 A farmer hired a labourer on this condition, that for every day he worked, he should receive 12d. but for every day he was idle he should be fined 8d. when 390 days were past, neither of them was indebted to the other; how many days did he work.

Suppose 1st. 140 working days,

390-140-250 idle

140X12=

2d. 150

240

1680 earned 150×12-1800

[blocks in formation]
« ΠροηγούμενηΣυνέχεια »