« ΠροηγούμενηΣυνέχεια »
6. What will 51 bbls. of cider cost, at 7 s. 6 d. per bbl. :
12£. 15 s.= cost, at 5 9. per bbl.
6£. 7s.6d. =cost, at 28. 6 d. per bbl. Ans. 19.£. 23. 6d cost, at 7 s. 6 d. per bhl
59. = £.) 51 ?s. 6 d. = } of 5 s.; then, 4 ) 12£. 15s.= cost, at 5 s. per bbl.
6.£. 7$. 6 d. ='cost, at 2s. 6 d. per bal
Ans. 19£. 2 s. 6 d. =cost, at 7 . 6 d. per bbl. II. Hence, when the price is not an aliquot part of 1£., we may first find what is the greatest even part, and then take parts of this part, and so on, for several times.
7. What will 20 yds. of cloth cost, at 12s. 6d. per yard?-12,10 8. What will 40 yards of eloth cost, at 15 s. per yard ?-30.
9. What will 36 bushels of corn cost, at 7s. 6 d. per bushel ?13,10. 10. What cost 12 bbls. of ale, at 17 s. 6 d. per bbl. ?-10,10.
A. 66£. 10 a. 11. Wkat will 5 cwt. 3 qrs. 21 lbs. of sugar cost, at $9,60 per cwt.?
2 qrs.= } cwt. $9,60
I qr. = 1 of 2 qrs.; thon, «
49,00 cost of 5 cwt.
Ans. $57,00 = cost of 5 cwt. 3 qrs. 21 Ia.
12. At $2,50 per yard, what will 5 yds. 2 qrs. of broadclotb cost ?-1375. What will 4 yds. 1 qr. cost ?-10625. Will 6 yds 3 qrs.?-16875. Ans. $41,25. 13. 5 cwt. 3 qrs. 16 lbs.,
at $4,20 per cwt. ?-2475. 14. 3 cwt. 1 gr. 7 lbs., at $3,60 per cwt. ?-11925. 15. 4 yds. 2 qrs., at $2,10"per yd. ?-945. 16. 4 gals. 2 qts., at $3,40 per gal. ?-1530. A. $61,425.
(LXXVII. 1. Two boys, William and Thomas, trading with marbles, in company, gained 80 cents; William owned of the marbles, and Thomas &; what was each une's part of the gain?
2. James and Rufus, owning a sled, in company, sold it for $3 more than it cost, that is, $3 gain; Rufus owned of it, and James }; what was each one's share of the gain?
Q. What is the Rule of FELLOWSHIP?
A. When men are trading in company, it ascertains the gain or loss to be shared by each.
Q. What is called Stock, or CAPITAL ?
1. Three men, A, B, and C, traded in company; A put in $200, B $400, and C $600 ; they gained $300 : what was each man's share of the gain?
In this example, it is evident, that B ought to have twice as much of the gain as A, for his stock is twice as much, and C 3 times as much as A ; that is, each man's gain or loss ought to have the same relation to the whole gain or loss, as the money he put in has to the money they all put in. The same prin ciple will apply in all cases in which a number is to be divided into parts, which shall have a given relation, or ratio, to each other, as the dividing a bankrupt's estate among his creditors, apportioning taxes, &c.
Hence, from the foregoing example, we derive the following proportions :
A's stock, $200
$400 1200 : 200 :: 300 : 50, A's gain C's stock,
1200 : 400 :: 300 : 100, B's gain. Whole stock, $1200
1200 : 600 :: 300 : 150, C's gain. By ratios. These are 1200, 1200, 1200,=
, =5,5, 3; then, 300 x , that is, of $300,= $50, A's; of $300 = $100, B's, ands of $300 $150,"C's gain.
Or, by analysis. If $1200 stock gain $300, then $1 stock will gain Tebo of $300,= 128=$1: Now, if $1 gain then 4 of $200, A's stock, = $50, A's gain; of $400, stock,=$100, B’s gain; and 1 of $600, C's stock, =$150, C'S gain.
This last method will generally be found the shortest, and best adapted to business; especially when there are several statements, in which all the first worms are alike, and all the third terms are alike.
Proof. It is plain, that, if the work be right, the amount of the shares of the gain or loss must be equal to the whole gain or loss; thus, in the last cxample, A's is $50 + B's $100+ C's $150= $300, the whole gain.
Q. What, then, is the Rule?
A. As the whole stock : to each man's stock :: the whole gain : to each man's gain.
2. Three merchants, A, B, and C, gained, by trading in com pany, $200; A's stock was $150, B’s $250, and C's $100 what was the gain on $1, and what was each man's share of the gain ? A. The gain on $1 is $4; then, of $150= $37,50, A's; of $250 = $62,50, B's; and of $400
$100, C's. 3. A, B, and C, freight a ship with 270 tons; A shipped on board 96 tons, B 72, and C 102; in a storm, the seamen were obliged to throw 90 tons overboard; what was the loss on I ton? and how many tons did each lose ? A. The loss on 1 ton is of a ton; A's, 32; B's, 24; C's, 34.
4. A and B trade in company, with a joint capital of $600 ; A put in $350,50, and B $249,50, and, by trading, they gained $120: what is the gain on $1, and what is each person's share of the gain? Ans. $}; A's, $70,10 ; B's, $49,90.
5. A ship, valued at $25200, was lost at sea, of which I belonged to A, ) to B, and the remainder to C: what is the losu on $1? and how much will each man sustain, supposing $18000 of her to be ensured ? Ans. $ ; A's, $2400; B's, $3600, and C's, $1200.
Perform the following examples, in the same manner, by finding how much it is for $1, or unity.
6. A detachment, consisting of 5 companies, was sent into a garrison, in which the duty required 228 men a day : the first company consisted of 162 men; the second, 153; the third, 144? the fourth, 117; and the fifth, 108 ; how many men must each company furnish, in proportion to the whole number of men? A. The proportion for 1 man is }; then, $ of 162 = 54, first company; the second, 51 : the third, 48; the fourth, 39; and the fifth, 36 men.
7. Two men, A and B, traded in eompany, with a joint capital of $1000 : they gained 400, of which X took $200, and B the remainder : what was each person's stock? Ans $1 gain requires 2 stock : A's, $750 ; B's, $250.
8. Divide $1000 between 4 persons, so that their shares inay be to each other as 1, 2, 3, 4. A. $100, $200, $300, $400.
9. A bankrupt is indebted to A $350, to B $1000, to C $1200, to D $420, to È $85, to F $40, and to G $20; his whole estate is worth no more than $1557,50 : what will be each creditor's part of the property?
In adjusting claims of this nature, it is the general practice to find how much the debtor pays on $1, which is, in this case,
A. A, $175; B, $500; Č, $600; D, $210 ; E, $42,50; $20; G, $10.
10. A wealthy merchant, at his death, left an estate of $30000, to be divided among his 5 children, in such a manner that their shares shall be to each other as their ages, which are 7, 10, 12, 15, 16 years; what was the share of each?
Ans. $3500, $5000, $6000, $7500, $8000. 11. A and B invest equal sums in trade, and clear $220, of which A is to have 8 shares, because he spent all his time in managing the concerns, and B, only 3 shares : what is each man's gain? and how much is A allowed for his trouble? Ans. $160; A's share, $100 for his trouble; $60, B's share.
12. If a town raise a tax of $1920, and all the property in town be valued at $64000, what will that be on $1? and what will be A's tax, whose property is valued at $1200 ? Ans. $,03 on a dollar ; A's tax, $36.
In assessing taxes, we must first make an inventory of all the property, both real and personal, of the whole town, and also of each individual who is to be taxed; and, as the whole number of polls are rated at so much each, the lux on all the polls must first be taken out from the whole tax, and the remainder is to be assessed on the property. Then, to find how much any individual must be taxed for his property, we need only find how much the remainder of the whole tax is on $1, and multiply his inventory by it.
Note.--In some states, taxes are assessed only on the real and personal estate of the inhabitants, no poll taxes being allowed.
13. A certain town is taxed $2140; the whole property of the town is valued at $500000; there are 200 polls, which are taxed $,70 each; A's property is valued at $1400, and he pays for 2 polls :
$ cts. Polls C's, at 1200, pays for 2; H's, at 825,50, pays for 3; D's, “ 1265, «
J's, “ 375,25, 66 1
2; K's, “ 265,30, What will be the tax on $1? and what will be A's tax? 200 polls X $,70 $140, amount of the poll taxes; and $2140 – $140= $2000, which is to be assessed on the property. $500000 - $2000 :: $1 : $,04, tax on $1. Then, to find A's tax, his inventory being $1400, we proceed thus :
$1400 X $,04 =$56
$57,40, A's whole tax, Ans
What will be C's tax ?-4940. What D's?-5130. What E's: 8710. What Fs?-14624. What H's ?-3512. What I's334160. What J's ?-1571. What K's?-12012.
1 LXXVIII. 1. Two men hired a pasture for $9; A put in 2 oxen for 6 months, and B 3 oxen for 5 months; what ought each to pay for the pasture ?
2 oxen for 6 months is the same as (2 X 6=) 12 oxen for 1 month; and 3 oxen for 5 months is the same as (3 X5=) 15 oxen for 1 month.
The shares of A and B are the same as if A had put in 12 oxen, and B 15, for 1 month each; hence the relation of 12 to 15 is the same as in Simple Fellowship, thus,
2 x 6=12
27 : 15 :: 9 : $5, B's.
Q. How, then, does Compound differ from Simple Fellowship ! A. Compound regards time, Simple does not. Q. From the preceding example, what appears to be the
RULE ? A. Multiply each man's stock by the time it is continued in trade.
Then, As the sum of the products : each man's product :: the whole gain or loss : each man's gain or loss.
Morc Exercises for the Slate. 2. Three merchants, A, B, and C, enter into partnership; A puts in $60 for 4 mo., B $50 for 10 mo., and C $80 for 12 mo.; but by misfortune they lose $50 : how much "loss must each man sustain ?
C's, $28,235+. 3. Three butchers hire a pasture for $48; A puts in 80 sheep
B 60 sheep for 2 mo., and C 72 sheep for 5 mo.; what share of the rent must each man pay? A's, $19,20.
Ans. B's, $ 7.20.
for 4 mo.,