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4. Tell me what sum, in sterling money, is just equal to $2466,33cts. 3 mills.
Ans. £554 18s. 6d.
RULE OF THREE.
The Rule Of Three teaches to find a number having the same proportion to a given number, that two other given numbers have between themselves. For this reason it is sometimes called the Rule of Proportion. It is called the Rule of Three, because in each of its questions there are given three numbers at least. And because of its excellent and extensive use, it has been often named the Golden Rule.
Rule.- Write down the number, which is of the same kind with the answer or number required.
Consider whether the answer ought to be greater or less than this number; if greater, write the greater of the two remaining numbers on the right hand of it for the third, and the other on the left for the first number or term ; but if it ought to be less, write the less of the two remaining numbers in the third place, and the other in the first.
Multiply the second and third terms together, divide the product by the first, and the quotient will be the answer.
Note 1.-It is sometimes most convenient to multiply and divide as in Compound Multiplication and Division. But when it is not, then reduce each of the compound terms to the lowest denomination mentioned in it, and reduce the first and third to the same denomination ; then will the answer be of the same denomination with the second term. And the answer may afterwards be brought to any denomination required.
2. When there happens to be a remainder after the division, reduce it to the name next below the last quotient, and divide by the same divisor; so shall the quotient be so many of the said next denomination ; do this as long as there is any remainder, or till you have reduced it to the least name, and all the quotients together 3. If the first term, and either the 2d or 3d, can be divided by any number, without remainder, let them be divided, and the quotients used instead of them.
will be the answer.
4. There are four other methods of operation besides the general one above delivered, any of which, when possible, performs the work much shorter than it. They are thus :
First, Divide the 2d term by the 1st, multiply the quotient by the 3d, and the product will be the answer.
Second, Divide the 3d term by the 1st, multiply the quotient by the 2d, and the product will be the answer.
Third, Divide the 1st term by the 2d, divide the 3d by the quotient, and the last quotient will be the answer.
Fourth, Divide the 1st term by the 3d, divide the 2d by the quotient, and the last quotient will be the answer.
Two or more statings are sometimes necessary, which may always be known from the nature of the question. The method of proof is by inverting the question.
EXAMPLES. 1. What is the value of 215. 6oz. 19dwt. of gold, at £3 19s. Ild. an ounce ? £. s. d.
th. oz. dwt.
2 6 19
12)296810 Pence, which divided by 12 and
20, gives the answer in pounds, 2,0)247,3s. 5d. &c.
Ang. £123 13g. 526d.
2. If 91. of tobacco coșt 1 dollar 20 cents, what will 25tt; cost?
$3,33] Ans. 3. If 2515. of tobacco cost $3,33}, what will 91t. cost ? H. $. cts. H.
25)3000(120 cents, or $1,20 the An.
0 4. What is the value of a firkin of butter containing 5615. at 10 d. per pound!
£2 9 0 0 the Answer. 5. If 7cwt. lqr. of sugar cost 36dols. 10c., what will be the price of 43cwt. 2qr. ?
Ans. 8216, 60c.
1444 2527 361
6. If 6 horses eat 21 bushels of oats in a month, how many bushels will 20 horses eat in the same time. ?
Hor. Bus. Hor. Bus.
70 Ans. 7. A man bought sheep Idol. llcts per head, to the amount of 51dol. 6cts: how many sheep did he buy?
sh. 1,11 : 1 :: 51,06 46 Ans. 8. What is the value of an cwt. of sugar at 5d. per 1., 25ft. a qr. ? th
Ho. £. s. d.
100 2 5 10 Ans. 9. How much in length of that which is 43 inches broad will make a square foot ? Breadth. Length. Breadth. Length. 41 12
12 2ft. 8in. Ans. 10. Bought 6 casks of raisins, each weighing 1cwt. 14. 12 lb. ; what will they come to at £2 ls. 8d. per cwt. ? Cwt. £ s. d. Cwt. qr. th.
£ s. d. 1: 2 18
1 1121 +6 : 17 0 43+ Ans. 11. If a man spend 2 dollars 45 cents a week, what will it amount to in a year
2,45 365 127,75 Ans. 12. What is the value of a pipe of wine at 101d, per pint? Pint. d. Pipe.
£. I 102 :: 1
44 2 Ans. 13. How many quarters of corn can I buy for 280 dollars, at of a dollar per bushel ?
Ans. 52 quarters, 4 bushels. 14. What is the value of 2qrs. Ina. velvet, at 19s. 8 d. per ell English ?
Ans. Ss. 10 d. 1 15. Suppose 18 yards of broadcloth 1}yds. wide is to be lined with shalloon that is of a yard wide ; how many yards of shalloon will be sufficient? Ans. 36 yds.
16. If 52 yards of cloth cost 156 dollars, how much will 4 yards cost ?
Ans. 12 dollars, 17. Bought 36 yards of cloth for 108 dollars, and sold the same at 3} dollars per yard; how much did I gain?
Ans. 18 dollars.
to the qr
18. If 7yds. of ribbon cost 3s. 4d., what will 126yds. cost ?
Ans. £3. 19. If a man earn 64 dollars in 4 months, how long must he work at the same rate to pay a debt of 300 dollars ?
Ans. 18 months, 3 weeks. 20. If an ounce of silver be worth 1 dollar, 10 cents, what is the value of 10 silver spoons, each weighing loz. 4 pennyweights ?
Ans. 13dolls. 20cts. 21. If 8f yards cost 4 dollars 20 cents, what will 131 yards cost ?
Ans.6dolls. 48cts. 22. How long will it take 5 men to do the same work which 37 men can do in 15 days ? Ans. 111 days.
23. what will 4 hogsheads of wine come to containing, viz. 791, 841, 1014, and 112 gallons, at 6s. 9d. per gallon !
Ans. £127 4s. 9d. 24. Bought 3hhds. of sugar, each weighing scwt. 1qr. 12tt. at 7dolls. 26cts. per cwt; what come they to, 25th. ?
Ans. $182,29c. 8 m. 25. If a chest of hyson tea weighing 7911. neat, cost £32 11s. 9d., what is it per pound ? Ans. 8s. 3d.
26. B owes £2119 17s. 6d., and he is worth but £1324 18s. 54d.; if he delivers this to his creditors, how much do they receive on a pound?
Ans. 12s. 6d. . 27. A merchant failing in trade, owes in all 29475 dollars, and delivers up his whole property worth 21894 dollars, 3 cents; how much per cent. does he pay; and what is B's loss to whom he owed 325 dollars ?
Ans.--He pays $74,28cts. per cent.
and B loses $83,59cts. 28. If a staff, 4 feet, 8 inches in length, cast a shadow 6 feet; how high is that steeple whose shadow is 153 feet ?
Ans. 119 feet. 29. Bought 270 quintals codfish for 780 dollars ; freight 37 dollars, 70cts. ; wharfage, truckage and other expenses 30 dollars, 60cts. ; at what must I sell them per quintal, so as to gain 143 dollars on the whole ?
Ans. 83,67cts. Im. + 30. If of a farm cost $1081, what is the whole worth ? fif. $. fif.