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7. Received per ship Napoleon, from South America, 55 bags of coffee, the gross weight of which is 220lbs. each, and the weight of each sack is 5lbs. ; required the net weight and value of the coffee at 16 cents per pound?

Ans. net weight 11825lbs.; value D1892.

8. Received from Salina 72 bags of salt, the weight of each bag is 210lb. gross, and each sack weighs 7lbs.; what is the net weight, and what does it come to at 4 cts. per pound?

Ans. weight 14616lbs.; value D584.64.

9. Boug it 110 hogsheads of sugar, gross 723lbs. each, weight of each hogshead 62 lbs.; what is the net weight, and what will it come to at 12.5 cts. per pound?

Ans. 72710lbs. ; amount D9088.75. 10. Bought 5 casks of rice, which weighed gross 18 cwt., 2 qrs., 12 lbs., tare per cask 45 lbs., for which I paid D5.50 per cwt., and sold the same for D6.25 per cwt.; required the net weight, cost, amount it sold for, and profit?

Ans. net weight 1859 lbs.; cost D91.29; sold for D103.74; profit D12.45.

REVIEW.

What is gross weight? What is tare? Repeat rule 1st. Repeat rule 2d.

What is net weight?

UNITED STATES DUTIES.

In all civilized countries, where merchandise or goods are imported, importers are required to pay a certain amount of their value, at a certain rate per pound, hundred, yard, or gallon; this is called duty, which is established and collected by the laws of the country where the goods are landed; for this purpose, customhouses are erected in the seaport towns to collect the custom or duties, tonnage of vessels, port duties, &c., which together are called the revenue. An ad-valorem duty is such a per cent. on the actual cost of the goods in the country from which they are imported; thus an ad-valorem duty of 20 per cent. on tea from China, is a duty of 20 per cent. on the cost of the tea in China; the duties are computed on the net weight.

EXAMPLES.

1. What is the duty on 1400 lbs. of coffee at 21 cts. per lb. ? Ans. 1400×24D3.50

2. If the duty on molasses is 5 cents on a gallon when im ported in an American vessel, and 10 per cent. more in a foreigr vessel; what is the duty on 3950 gallons in both vessels?

Ans. D197.50 and D217.25 3. What is the duty on goods which cost in Calcutta D2780.50, at 12 per cent. ad valorem ? Ans. D347.561

POSITION.

POSITION is a rule founded on the principles of proportion, and by working with one or more supposed numbers, as real numbers, we can discover the true number or answer to the question. It is of two kinds, termed single and double. Single Position is when only one supposed number is necessary for the operation. Such questions as are usually given in arithmetic for solution, by working with supposed (improperly called false) numbers, are equations in algebra, by which they are more conveniently and readily solved by those who are acquainted with that science. (For an illustration of the rule, see Double Position.)

SINGLE POSITION.

RULE.

SUPPOSE a number, and work with it as though it was the true number, according to the nature of the question; then, as the result of that operation is to the given number :: so is the number supposed to the number required. Proof, add the several results together.

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Suppose debt D1200 1300 ) then, 650: 500 :: 1200

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2. A certain sum of money is given to 4 persons: to A. 3, B., C., and D. draws the rest, which is D28; required the (This question can be solved by Double Position.) Suppose 60,20 A. Then, 15: 28: 60: 112. Ans. Proof, 112, 37.33 A.

sum.

45 115 B.

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3. What sum is that of which 3, 1, and †, make D94 ?

Ans. D120. 4. A person said that, 1, †, and of the money in his possession would make D57; how much had he? Ans. D60. 5. The ages of A., B., and C., amount to 133 years; B. is } older than C., and A. is older than B.; required their separate ages. Ans. A. 56 yrs., B. 42 yrs., C. 35 yrs. 6. What sum of money at 6 per cent. per annum, simple interest, will amount to D500 in 10 years? Ans. D312.50. B.'s age is 1.5 of A.'s, C.'s twice as much as B.'s, and their united ages make 132 years; required the age of each? Ans. A. 24, B. 36, C. 72 years.

8. What is the age of a person who says that if of the 용 years he has lived be multiplied by 7, and of them be added to the product, the sum would be 292? Ans. 60 years.

9. A bankrupt is indebted to A. D284.60, to B. D794.18, to C. D651.44, and to D. D491.25, and his estate is worth D1460.5; if the whole were divided, how much would each creditor receive?

DOUBLE POSITION

Teaches to solve such questions as require two supposed numbers in the operation.

RULE I.

SUPPOSE two numbers, and work with each agreeably to the tenor of the question, observing the errors of the results; multiply the errors of each operation into the supposed number of the other; then, if the errors be alike (that is, both too much, or both

too small), take their difference for a divisor, and the difference of the products for a dividend; but if not alike, then take their sum for a divisor, and the sum of the products for a dividend.

QUESTIONS.

1. A., B., and C., agree to pay a debt of D500, of which A. is to pay a certain sum; B. is to pay D10 more than A., and C. is to pay as much as both A. and B.; how much must each one pay? Suppose 1st, A. 90 Suppose 2d, A. 100 500 500

B. 100

C. 190

Sum 380

B. 110-380 -420

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Then, 120 error, × 100 A=.12000 80 error, X 90 A.= 7200

Difference of error,

500 proof.

Note. This rule is founded on the supposition that the first error is to the second, as the difference between the true and supposed number is to the difference between the true and second supposed number. When that is not the case, the exact answer to the question can not be found by this rule.

RULE IT.

15 15 10

7

1. Take any two convenient numbers and proceed with each according to the conditions of the question. 2. Place the result or errors against their positions or supposed numbers, thus X and if the error be too great, mark it with +; if too small, with 3. Multiply them crosswise; that is, the first position by the last error, and the last position by the first error. 4. If the errors be alike, that is, both too small or both too great, divide the difference of the products by the difference of the errors, and the quotient will be the answer. 5. If the errors be unlike, that is, one too small and the other too great, divide the sum of the products by the sum of the errors, and the quotient will be the answer.

Note. When the errors are the same in quantity, and unlike in quality, half the sum of the supposition is the number sought Observe the following examples and explanation.

EXAMPLE 2. (1st ques.)

Supposition 1. A. 90 Sup. 2. A. 100 given num. 500

B. 110 am. of sup. 380

B. 100

C. 190.

C. 210

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500

420

1 er'r 120 2 er. 80

12000 -7200

[d.er. 40)4800(120D. A. p'd

12000 7200

EXAMPLE III.

130 B. "

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When the errors are unlike, that is, one plus and the other minus ̧

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2. A. is 20 years of age; B.'s age is A.'s, and half of C.'s; and C's is equal to them both; their several ages are required. Ans. A. 20, B. 60, C. 80.

3. Three persons pay the sum of D100; B. paid D10 more than A., and C. as much as A. and B.; how much did each pay? Ans. A. 20, B. 30, C. 50. 4. What sum is that, which being increased by its 2, its, and 18 more, will be doubled?

Ans. 72.

5. A., B., and C., receive D324, but not agreeing in the division of it, each took as many as he could: A got a certain number; B. as many as A. and D15 more; C. got a fifth part of the sums added together; how much did each get?

Ans. A. D127.50, B. D142.50, C. D54. 6. Divide D100, so that B. may have twice as much as A., wanting D8; and C. three times as much, wanting D15; what is the share of each? Ans. A. D20.50, B. D33, C. D46.50. .

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