« PreviousContinue »
2. Reduce $952,38 to livres of France.
Thus, 95238cts.=190476 half-cts.; then 18 cts.=37 half-cents, and 190476-37=5148 livres, Ans. 3. Reduce 987 Francs to Federal money.
Ans. $185,061 4. Reduce 2540 Florins to Federal money. Ans. $1016. 5. Reduce $195,20 to Florins.
Ans. 488. 6. Reduce 145 Tales of China to Federal money.
A Pound Sterling of Great Britain,
RULE OF THREE DIRECT. 1. The Rule of Three Direct teaches from three given numbers to find a fourth, which shall have the same proportion to the third, as the second has to the first.
2. Of the given numbers, the first two are a supposition and the last (which may be known by the words, what cost ? how much ? how far ? how many ? &c.) is a demand.
3. In stating questions in the Rule of Three, two of the given numbers, that is, the first and third, must always be of the same name or kind; and the second or middle term must be of the same name or kind with the answer or term sought.
Sign. :: Four points set in the middle of four numbers, denote them to be proportional to one another by the Rule of Three, thus; 2:4::8:16 is read, As 2 is to 4 so is 8 to 16.
1. State the question so that the first and third terms will be of the same name or kind, and the second or middle term of the same name or kind with the answer.
2. Bring the first and third terms to the same denomina
tion, and reduce the middle term to the lowest name mentioned in it.
3. Multiply the second and third terms together, and divide the product by the first term; the quotient will be the answer in the same denomination you left the middle term in; which may be brought into any other denomination required.
Proof.—The method of proof is by inverting the question.
1. If 8 yards of cloth cost 12 dollars, what will 20 yards cost?
must possess the third place; then 12
8 yards being the same kind, is the 8)240 first term; and 12 dollars is the se
Ans. $30 cond term. Then the second and third terms multiplied together, and the product divided by the first term; the quotient is 30 dollars, which bears the same proportion to 20 yards, that 12 dollars does to 8 yards.
2. If $30 will buy 20 3. If 20 yards cost $30, yards, how many yards will what cost 8 yards ? $12 buy?
yds. dols. yds. yds.
20 : 30 ::8 30 : 29::12
Ans. 12 dols. Ans. 8 yards. 4. If 12 dollars will buy 8 yards of cloth, how many yards will 30 dollars buy? dols. yds.
It will be seen that the pre12 : 8:: 30
ceding sums are all similar.8
The different results are made 12)240
by changing the order of the Ans. 20 yds. terms. 5. If 3 ewt. of sugar cost $33 60, what will 12cwt. 2qrs. 14lbs. cost?
cts. cwt. gr. lbs. 3: 33 60 :: 12 2 14 112
State the question as 336
before ; then as the first 28
and third terms must be 404
of the same name, we 101
reduce them both to lbs. 1414
Then multiply the se
cond and third terms to. 3360
gether, and divide the 84840
product by the first term, 4242
and the quotient or an4242
swer, is 141 dollars, 40 336)4751040(14140 cents. 336
Note.In multiplying 1391
and dividing dollars, cts, 1344
&c. observe the rules
already taught for multi 470
plying and dividing de 336
cimals, or Federal mo, 1344
00 2. When the first and third terms are Federal money, you may reduce them to the same denomination by annexing as many ciphers, (when necessary) as will make their decimal places equal. Then multiply and divide as in whole num: bers, and the quotient or answer will be of the same name or denomination of the middle term.
6. If 5 dollars will buy 4 bushels of wheat, how many bushels can I buy for 118 dollars 75 cents.
In this example, the first 500 : 4 :: 11875
term being dollars, and the 4 bush.
third term being dollars 500)47500(95 Ans. and cents, therefore, we 4500
reduce them both to cents, 2500
then multiply and divide 2500
as before. 7. If 3 pairs of stockings cost $1 75 what will 3 dozen pair cost ?
per cwt. ?
8. If 3 dozen pairs of stockings.cost $21, what will 3 pairs cost ?
Ans. $1 75 9. If $1275 buy 17 yards of cloth, how many yards can I buy for $2 25 at the same rate ?
Ans: 3 yards. 10. At 15cts. per lb. what will a firkin of butter come to, weight 54 lbs.
Ans. $8 10. 11. If 6 horses eat 21 bushels of oats in one week, how many bushels will serve 20 horses the same time?
Ans. 70 bushels. 12. Bought 6 chests of sugar, each weighing 8 cwt. 3 qrs., what do they come to at $8 50
Ans. $446 25. 13. If 12 months or one year's wages be $225 58, what will 5 months' wages be, at the same rate ?
Ans. $93 99 15. 14. If a man lay out $211 25 in merchandise, and thereby gain $68 50, how much will he gain by laying out $25, at the same rate ?
Ans. $8 10 6.10 15. If I pay $71 50 for 11 barrels of flour, how many barrels can I have for $1014?
Ans. 156 barrels. 16. What will 4 tierces of rice come to, each weighing 7cwt. 2qrs. 141b., at $9,35 per cwt. ?
Ans. $285 17cts. 5m. 17. If a man's yearly income he $756, 65cts., what is that a day?
Ans. $2,07c. 3m. + 18. If 8 yards of cambric cost $5,48, what must be given for 25 pieces, each containing 27) yards ?
Ans. $470, 93c. 7 fom, 19. If 100 dollars in 1 year gain 6 dollars, what will 385 dollars gain in the same time ?
Ans. $23, 10c. 20. A owes B 1234 dollars, but not being able to pay the whole, B agrees that if he will pay him 57 cents on a dol: lar he will release him; how much must B receive ?
Ans. $703,38. 21. If 35 dollars will pay for 4cwt. of sugar, how much may be had for 215 dollars 19 cents at the same rate ?
Ans. 24cwt. 2qrs. 10lb. 6318 oz. 22. If 'I give 1887 dollars for 148 acres of land, how many acres can I buy for $63,75 at the same rate ?
Ans. 5 acres.
23. When a tun of wine cost 140 dollars, what cost 3 quarts ?
Ans. 41cts. 64.m. + 24. Bought a bale of cloth for 436 dollars 80 cents, at the rate of 7 dollars for 5 yards ; how many yards did it contain ?
Ans. 312 yards. 25. A merchant bought 4 hogsheads of wine, containing 61, 63, 63) and 64 gallons, at 1 dollar 56 cents per gallon ; what was the cost of the whole ?
61 +63+63}+64=251]gals. Ans. $392,34. 26. If a man's income be 1296 dollars a year, and he spend 2 dollars 37] cents a day during the year, how much will he have saved at the year's end ?
Ans. 429 dols. 12 cts. Sterling Money.
EXAMPLES. 27. If 3 yards of cloth cost 45s., how many yards may I have for £16 10s. at the same rate ?
The first and third 330
terms must be reduced 3
to the same denomi. 45)990(22yds. nation, &c.
90 90 90
28. If 1 yard of cambric cost 12s., what cost 4 pieces, each measuring 20 yards ?
Ans. £48. 29. A grocer bought a hogshead of sugar, weighing 8 cwt. 3qrs., at 6d. per pound; what was the cost of it?
Ans. £24 10s. 30. How much sugar can I buy for £24 10s., at 6d. per pound?
Ans. 8cwt. 3qrs. 31. If 58 yards of cloth cost £18 178., what is that per Ell English?
Ans. 8s. 1 d. 32. Ă owes B £3475, but B compounds with him for 13s. 4d. on the pound; what must B receive for his debt ?
Ans. £2316 13s, 4d.