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RULE OF THREE DIRECT. TUE Rule of 'Three Direct Teaches, by having three numbers given to find a fourth, which shall have the same proportion to the third, as the second has to the first.
1. Observe that two of the given viumbers in your question are always of the same name, or kind; one of which must be the first number in stating, and the other the third number; consequently, the first and third numbers must always be of the same name, or kind; and the other number, which is of the same kind with the answer, or thing sought, will always possess the second or middle place.
2. The third tern is a demand ; and may be known by these or the like words before it, viz. What will ; What cost? How many ? llow far? How long ! or, How much ? &c.
RULE. 1. State the question; that is, place the numbers se that the first and third terms may be of the same kind; and the second term of the same kind with the answer, or thing sought.
2. Bring the first and third terms to the same denomination, and reduce the second term to the lowest name mentioned in it.
3. Multiply the second and third terms together, and clivide their product by the first term; the quotient will be the answer to the question, in the same denomination you left the second term in, which may be brought into any other denomination required.
The method of proof is by inverting the question.
NOTE.--The following inethods of operation, when they can be used, perform the work in a much shorter manner than the general rulc.
1. Divide the second term by the first; multiply the quotient into the third, and the product will be the answer. Or
2. Divide the third term by the first; multiply the quotient into the second, and the product will be the answer. Or
9. Divide the first term by the second, and the third oy that quotient, and the last quotient will be the answer.
Or 4. Divide the first term by the third, and the second by mat quotient, and the last quotient will be the answer,
1. If 6 yards of cloth cośť9 dulars, what will 20 yards cost at the same rate ?
Yds. Here 20 yards, which moves
6:9: : 20 the question, is the third term;
9 6 yds. the same kind, is the first, and 9 dollars the second.
Ans. 830 2. If 20 yards cost S0 dols. 3. If9 dollars will buy 6 what cost 6 yards?
yards, how many yards will Yds. 8 Yds 30 dollars buy? 20 : 30 ::6
9) 180 Ans. 89
Ans. 20yds. 4. If 3 ewt. of sugar cost 81. 83. what will 11 cwt. I qr. 24 lb. cost! S cwt. 8l. 85. C.
lb. 112 20 11 1 24 As 336 : 168 : : 128416. 4
168 336 lb. 168s. 45
336) 215712 64,2
2016 1284 lb
-321.2s. 1411 Ans. 1344
5. If ane pas ofertar un cost 43. Gu. what will 19 rozch'paqr cost?:
Ans. 651 6s. 6:11:19 dozen pair
of shoes cost 511. 6s. what will one pair cost:
Ains. 4s. 6d. 7. At 10d. per pound, what is the value of a firkin of butter, weight 56 pounds ?
Ans. £ 9 9s. 8. How much sugar can you buy for 231. 2. at 94. a pound?
Ans. '5C. 2qrs. 9. Bought 8 chests of sugar, cach 9 cwt. 2 qrs. what do they come to at 21. 5s. per cwt. ? Ans. £,171.
10. If a man's wages are 751. 10s. a year, what is that a calendar month?
fils. £6 5s. 10d. 11. If 44 tons of hay will keep 3 cattle over the winter; how many tons will it take to keep 25 cattle the same time?
Ans. 37) tons. 12. If a man's yearly income be 2081. 1s. what is that a day?
ins. 11s. 4d. 33qrs. 15. If a man spends is. 4d. per day, how much is that a year?
Ans. £00 105. 8d. 14. Boarding at 125. 60. per week, how long will sel. 10s. last me
fls. 1 year. 15. A owes B 34751. but I compounds with him tok ? 35. 4d. on the pound; pray what'niust lie reccive for his debt ?
Ans. £,2316 15s, 4d. 16. A goldsmith sold a tankard for gl. 19s. at 5s. 49. per ounce, what was the weight of the tankard :
Ans. 2l. 8oz. 5peto 17. IT 2 cut. Sqrs. 01 16 of sugar cost 61. Is. Sú. what cost 351 cut.?
Ins. £75. 18. Bought 10 pieces of cloth, each piece containing . 9% yards, at 11s. 4. pence per vard; what did the whole
Ans. $5.9. O.
come to :
NOTE 1. You must state the question, as taught in the Rules foregoing, and after reducing the first and third Terms to the same name, &c. you may multiply and divide according to the rules in decimals; or by the rules Cor multiplying and dividing Fetteral Money:
EXAMPLES, 19. If 7 yd's, of cloth cost 15 dollars 47 cents, what will 12 yds. cost? Yds. Scis. yds.
7 : 15,47 : :12
ins. 26.50-S96. 52cis. But any sum in dollars and cents may be written down as a whole number, and expressed in its lowest denomistation, as in the following example: (See Reduction of Federal Money, page 67.)
20. What will i qr. 9 lb. sugar come to, at 6 dollars 45 cts. per civt. :
cts. 1 9
As 112 : 645 :: S,
- et, 119) 23865(2134. Ans. :82, 19.
9 NOTE 2. When ihe first and third numbers are federal money, you may annex cyphers, (if necessary) until you make their decimal places or figures at the right hand of the separatrix, equal: which will reduce them to a like denomination. Then you may multiply and divide, as in whole numbers, and the quotient will express the answer in the least denomination mentioned in the second, or middle terin.
24. If 3 doliars will buy 7 yards of cloth, how many yards can I buy for 120 dollars, 75 cents ?
cts. yds. cts. As S00 : 7 :: 12075
300)84525(2814 Ans 22. If 12 lb. of Tea cost 6 do's. 600 78 cts. and 9 mills, what will 5 lb). cost at the same rate ?
2452 th. anills. lh.
2400 As 12 : 6739 : : 5
$ cts. 23. If a man lays out 121, 23 in merchandize, and thereby gains 59 dollars, 51 cts. how much will he gaia by laying out 12 dollars at the saine rate ?
Cents. cents. cenis.