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191. 135. 3d. the answer. g. 2733 at 28. 6d.
Ans. 341. 38. rd. 4. 9371 at 31. 175. 8d.
Ans. 36401. 125. 60. 5. 37cwt. 2qrs. 14lb. at 71. ros. od. per cwt.
Ans. 2831. 118. 11.
TARE AND TRETT.
TARE AND TRETT are practical rules for deducting certain allowances, which are made by merchants and tradesmen in selling their goods by weight.
Tare is an allowance made to the buyer for the weight of the box, barrel, or bag, &c. which contains the goods: bought, and is either at so much per box, &c. at so much per cwt. or at so much in the gross weight.
Trett is an allowance of 4lb. in every 1041b. for waste, dust, &c.
Cloff is an allowance of alb. upon every 3cwt.
Gross weight is the whole weight of any sort of goods, together with the box, barrel, or bag, &c. that contains them.
Suttle is the weight, when part of the allowance is deducted from the gross.
Net weight is what remains after all allowances are made.
CASE CASE 1.
When the tare is a certain weight per box, barrel, or bag, Sc.
RULE.* Multiply the number of boxes, or barrels, &c. by the tare, and subtract the product from the gross, and the remainder is the net weight required.
EXAMPLES. 1. In 7 frails of raisins, each weighing 5cwt. 2qrs. 5lb. gross, tare 231b. per frail, how much net ? 23 X 7=Icwt. Iqr. 21 lb. 4
: cwt. grs. Ib.
38 3 7 gross.
:37 I 14 the answer, 2. In 244 barrels of figs, each 3qrs. 19.b. gross, tarc colb. per barrel, how many pounds net ?
3. What is the net weight of 14 hogsheads of tobacco, each scwt. 2qrs. 1715. gross, tare scolb. per hhd. ?
Ans. 66cwt. 2qrs. 141b
When the țare is a certain weight per cwt.
Divide the gross weight by the aliquot parts of a cwt. contained in the tare, and subtract the quotient from the gross, and the remainder is the net weight.
* It is manifest, that this, as well as every other case in this role, is only an application of the rules of proportion and practice
cwt. grs. lb.
8 the answer. 2. What is the net weighof 7 barrels of .pot-ash, each weighing 201lb. gross, tare being at iolb. per cwt. ?
Ans. 128 11b. 6oz, 3. In 25 barrels of figs, each 2cwt. Iqr. gross, tare 161b, per cwt. how much net ?
Ans. 48cwt. 241b,
When Trett is allowed with Tare,
Divide the suttle weight by 20, and the quotient is the trett, which subtract from the suttle, and the remainder iş the net weight.
1. In gcwt. 2qrs. 171b. gross, tare 37lb. and trett as usual, how much net ?
cwt. qrs. lb.
9 17 gross.
8 25 the answer. 2. In 7 casks of prunes, each weighing 3cwt. iqr. 5lb, gross, tare 17 ib. per cwt. and trett as usual, how much net?
Ans. 18cwt. 2qrs. 251b.
3. What is the net weight of 3 hogsheads of sugar weighing as follows : the first, 4cwt. 5lb. gross, tare 731b. ; the second, 3cwt. 2qrs. gross, tare 56lb. and the third, 2cwt. 3qrs. 171b. gross, tare 471b. and allowing trett to each as usual ?
Ans. 8cwt. 2qrs. 41b.
Deduct the tare and trett, as before, and divide the suttle by 16$, and the quotient is the cloff, which subtract from the suttle, and the remainder is the net.
EXAMPLES 1. What is the net weight of a hhd. of tobacco, weighing 15cwt. 3qrs. 201b. 'gross, tare 7lb. per cwt. and trett and cloff as usual ?
cwt. qrs. lb.
14 I 4 the answer, 2. In 19 chests of sugar, each containing izcwt. Iqr. 171b. gross, tare 131b. per cwt. and trett and cloff as usual, how much net, and what is the value at 5d. per pound ?
Ans. 215cwt. 171b. and value 577!. 6s. 5.2.
COMPOUND PROPORTION teaches how to resolve such questions, as require two or more statings
Simple Pro portion.
In these questions there is always given an odd number of terms, as five, seven, or nine, &c. These are distin. guished into terms of supposition, and terms of demand, the number of the former always exceeding that of the latter by one, which is of the same kind with the term or answer sought.
This rule is often named the Double Rule of Three, because its questions are sometimes performed by two operations of the rule of three.
RULE* FOR STATING, 1. Write the term of supposition, which is of the same kind with the answer, for the middle term.
2. Take one of the other terms of supposition, and one of the demanding terms of the same kind with it, then place one of them for a first term, and the other for a third, according to the directions given in the rule of three. Do the same with another term of supposition and its correspondent demanding term ; and so on, if there be more terms of each kind ; writing the terms under each other, which fall on the same side of the middle term.
METHOD OF OPERATION. 1. By several operations.--Take the two upper terms and the middle term, in the same order as they stand, for the first stating of the rule of three ; then take the fourth number, resulting from the first stating, for the middle term, and the two next terms in the general stating, in the same order as they stand, for the extreme terms of the
* The reason of this rule for stating, and of the methods of operation, may be easily shewn from the nature of simple proportion ; for every line in this case is a particular stating in that rule. And, therefore, with respect to the second method, it is evident, that, if all the separate dividends be collected into one dividend, and all the dira ors into one divisor, their quotient must be the answer sought.