8. What is the neat weight of 8 hogsheads of tobacco, weigh. ing gross 86cwt. 2 qr. 24lb. tare 100lb. a hhd. Ans. 79cwt. 2qr. 8lb. 9. Sold 9 hogsheads of sugar, each 6cwt. 2qr. 12lb. gross, tare 861b. a hhd. at $9 75cts. a cwt. what is the neat weight and value? Ans. 52cwt. 2qr. 6lb. $512 39cts. 7m. 10. What is the neat weight, and value of 12 casks of raisins, each weighing 30wt. 2qr. 10lb. gross, tare 20lb. a cask, at £2 148. a cwt.? Ans. 40cwt. 3qr. 20lb. £110 10s. 11d. CASE 3. When the tare is so much per hundred weight. RULE. Deduct from the gross such aliquot part or parts of it, as the tare is of a cwt. the remainder will be the neat. Or, multiply the pounds gross by the tare per cwt. and divide the product by 112; the quotient will be the tare, which deduct as before. EXAMPLES. 11. In 12 butts of currants, each 7cwt. 1qr. 10lb., tare 1610. per cwt., how much neat? Ans. 75cwt. 1qr. 27lb: 12. What is the neat weight of 9hhd. of tobacco, each weigh ing gross 8cwt. 3qr. 14lb., tare 16lb. a cwt.? Ans. 68cwt. 1qr. 24lb. 13. In 83cwt. 3qr. gross, tare 20lb. a cwt., what is the neat weight? Ans. 68cwt. 3qr. 5lb. 14. What is the neat weight and value of 40 kegs of figs, gross -750wt. 3qr. 14lb., tare 14lb. a cwt. at $2 31cts. a cwt.? Ans. Wt. 66cwt. 1qr. 16lb. CASE 4. When tret is allowed with tare. RULE. 1. Find the tare as before directed, whide subtract from the gross, and call the remainder suttle. 2. Divide the suttle by 26,* and the quotient will be the tret, which subtract from the suttle, and the remainder will be the neat weight. EXAMPLES. 15. In a hogshead of sugar, weighing 10cwt. 1qr. 12lb. gross tare 14lb. per cwt., tret 4lb. per 104lb., how much neat weight Ans. 8cwt. 2qr. 24lb. 16. In 27 bags of coffee, each 2cwt. 3qr. 17lb. gross, tare 13lb. a cwt., tret 4lb, on 104lb., what is the neat weight? Ans: 66cwt. 245.42 lb. The reason of dividing by 26 is to shorten the operation of multiplying by 4 and dividing by 104, for 1044—26. 17. What is the neat weight of 17 chests of sugar, weighing 120cwt. 2qr. gross, tare 176lb., tret 4lb. on 104lb. ? Ans. 12808lb. or 114cwt. 1qr. 12lb. 18. Sold 177cwt. 22lb. gross, tare 9lb. a cwt., tret 4lb. on 104lb.; required the neat weight, and its amount at $9 25cts. Wt. 156cwt. 2qr. 22lb. Value, $1449 44cts. 1m.+ a cwt. Ans. APPLICATION. in 19. In 16 lugsheads of tobacco, each weighing 5cwt. 1qr. 19lb. gross, tare on a hhd. 100lb., how much neat weight? Ans. 72cwt. 1qr. 20lb. 20. In 8cwt. 3qr. 20lb. gross, tare 381b., tret 4lb. on 104lb., how much neat weight? Ans. b. neat. 21. In 14 hogsheads of tobacco, weighing gross 89cwt. 3qr 17lb., tare on a hogshead, 100lb., what is the neat weight and value at $4 75cts. a cwt.? gat 77cwf. 1qr. 17lb. Ans. Value, $367 65cts. 7m.+ 22. What is the neat weight of 5 casks of sugar, weighing as follows; viz. No. 1, 4cwt. 2qr. 14h. gross, tare 21lb.; No. 2, 3cwt. Oqr. 17lb. gross, tare 18lb.; No. 3, 5cwt. 3qr. 10lb, gross, tare 1qr. 11lb.; No. 4, 6cwt. 1qr. 16lb. gross, tare 271b.; No. 5, 3cwt. 2qr. 18lb. gross, tare 191b.; and what is the value, the three first at £2 4s. 7d. a cwt. and the other two at £2 17s. 6d. ? Wt. 22cwt. 2qr. 7lb. Value £56 10s. 51d.+ My Ans. 23. Sold 12 butts of currants, at $9 20cts. each butt weighing 7cwt. 1qr. 10lb. gross; tare 161b. a cwt. what is the neat weight and amount? Ans. Wt. 75cwt. 1qr. 27lb. Value $694 51cts. 7m. + THE DOUBLE RULE OF THREE. In the Double Rule of Three, five numbers or terms are given, to find a sixth; three of which are a supposition, and two, a demand. RULE 1. 1. Place that number or term which is of the same name or kind with the answer the third place. 2. Then take one term from the supposition, and one from the demand, both of the same name or kind, and place them with the third term, as directed in the Single Rule of Three. 3. Then proceed in the same manner with the two remaining terms. 4. Reduce the similar terms to the same denomination if ne cessary. 5. Multiply the terms in the second and third place together, and divide their product by the product of those in the first place: the quotient will be the answer or term sought. PROOF. By two statings of the rule of three: Or, invert the stating. Note. If either of the first terms, or both, will divide any of the three last, or can be divided by any of them, or by any other number without a remainder, the operation may be contracted by cancelling them, and using their quotients in their stead. 1. If 6 men in 8 days, eat 10lb. of bread, how much will 12 Or; State the question, by placing the three terms of supposi tion in the following order. 1. Let that which is the principal cause of gain, loss, or action be put in the first place. 2. That which relates to time, distance of place, and the like, in the second place. 3. And the remaining one in the third place. 4. Place the other two terms under those which are of the same name. 5. If the blank fall under the third term, then multiply the first and second terms for a divisor, and the other three for a dividend. 6. If the blank fall under the first or second term, multiply the third and fourth terms for a divisor, and the other three, for a dividend. EXAMPLES. 1. If 6 men in 8 days eat 10lb. of bread how much will 12 men 2. Suppose 4 men in 12 days mow 48 acres; how many acres ean 8 men mow in 16 days? Ans. 128 acres. Ans. 60 bushels. 3. If 10 bushels of oats be sufficient for 18 horses 20 days, how many bushels will serve 60 horses 36 days? 4. If 4 dollars be the hire of 8 men for days must 20 men work for 40 dollars? 5. If 200lb. be carried 40 miles for 40cts. how far may 20200lb. be carried for $60 60cts.? Ans. 60 miles. 6. If $100 in 12 months gain $6 interest, how much will $75 gain in 9 months? Ans. $3 37cts. 5m.+ 7. If the tuition of 3 boys for two quarters of a year, be $40 20 cents, how much will the tuition of 60 boys amount to for 41 years? Ans. $7236. 2 8. If $100 in one year gain $3 50cts. interest, what sum will gain $38 50cts. in one year and a quarter? 9. If $100 in 12 months gain $8 interest, in $750 gain $480? Ans. $880. what time will Ans. 8 years. 10. If 2 men can do 12 rods of ditching in 6 days, how many rods may be done by 8 men in 24 days? Ans. 192 rods. 11. An usurer put out $186 to receive interest for the same and when it had continued 3 months, he received for principa and interest $193 44cts. I demand at what rate per cent. per annum he received interest? Ans. 6 per cent. 12. If a footman travel 240 miles in 12 days, when the days are 12 hours long, how many days will be required to trovel 720 miles when the days are 16 hours long? Ans. 27 days. 13. If 3 masters, who have each 8 apprentices, in 5 weeks, each week 6 days, earn $360; how much will 5 masters, who have each 10 apprentices, earn in 8 weeks, each week 5 days, |