a pound of sugar cost of a dollar, what A. $32,4=$32.2663.

15

48. If cost 173 fb.? 49. If of a lb. of sugar, cost of a shilling, what will 3 of a lb. cost? A. 4d. 313 qrs. 50. If yd. cost £., what cost of an Eil English? A. 17s. 1d. 29 qrs.

51. If 1 cwt. cost 3£., what cost 9 lbs. ? A. 6s. 3 d. 52. A man owning of a vessel, sold of his share for $956.00 what was the vessel worth? Ă. $1,794.375. 53. If 34 cwt. of iron cost $145 what is that pr. cwt.? A. $47-$4.07%.

54. If of a yd. cost £., what cost of an Ell English. A. £178.2d.

55. If 75 lb. of butter cost $15, what cost 274 lbs. ? A. 581917-85.30341. 56. If by travelling 12 hours in a day, a man performs a journey in 7 days, how long will it take him, at the rate of 94 hours a day? A. 9173 days.

285

57. If of a yd. cost $13, what cost 17 yds. at that rate? A. $178.38.

58. A man sold 51, would 174 cwt. cost? 59. If bu. of corn rate. A. $0.952.

cwt. of sugar for $587.00 What A. $198.19443.

cost $3, what cost 11 bu. at that

60. If 3 of a barrel of flour cost 14£., what cost 43 barrels ? A. 93£. 9s. 7d. 29 qrs.

NOTE. When examples containing Fractions are solved by proportion, and the first term, or that by which it is necessary to divide, is a Fraction, this term may be inverted and used as a multiplier (§ LI. Rule 11.)

61. If of a bushel cost of a dollar, what cost 1 bushel. A. $0.561

62. If

63. If

64. If

what cost 1 cwt.? A. $933.

what cost 50 yds. ?

A. $31.25.

cwt. of sugar cost $, what cost 40 cwt.?

A. $82.274.

§ XCII. FELLOWSHIP, by analysis, has been already explained (§ XLIX.) Examples in Simple Fellowship may also be solved by Simple Proportion. No particular rule is necessary.

1. A, and P purchase goods in company, A laying out $350.00, and B, $470.00. They gain $250. How much should each have? Ans. A, $106.707+ B, $143.293

2. Three merchants trade, A furnishing $240.00, B $360.00, and C, 600.00. They gain $325.00. What is each one's share?

Ans. A's $65.00. B's $97.50. C's $162.50. 3. Four men trade, A furnishing $140.00, B, 260.00, C, $300, and D, $100. They gain $307. What is each one's share?

Ans. A's, $53.725, B's $99.775, C's $115.125, D's $38.375. 4. A and B trade and gain $100.00. A furnished $640.00 stock, and B, so much that he must have $60.00 for his share of gain. What amount of stock did B furnish? Ans. $960.00.

5. A, B, and C traded. A furnishes $140.00, B, $250.00, and C, 120 yds. of cloth at cost. They gained $230.00, of which $100 fell to C as his share. What was the cost of C's cloth per yd.? Ans. $2.50 per yd.

6. In a trading company, A puts in $175.00 capital, B, $200.00, and C, $500.00. They lose $250.00. What is each one's loss? Ans. A's $50.00, B's $57.142, C's $142.8574.

In the same manner, money or property, which is to be shared in a given ratio by several individuals, may be divided. This comprehends the division of an insolvent debtor's estate, the distribution of prize money, dividing an inheritance among heirs in a given ratio, the assessment of taxes, &c. &c. It will be observed that all these calculations may be made analytically, as well as by proportion.

7. A captain, mate and 20 seamen took a prize worth $3,501.00, of which the captain takes 11 shares, the mate 5 shares and each sailor 1 share. What must each have?

Ans. Capt. $1,069.75. Mate $486.25. Each sailor $97.25. 8. Divide the number 360 into parts which shall be to each other as 2, 3 and 4. Ans. 80; 120; 160.

9. Three persons share $600.00, so that the second has twice as much as the first; and the third, twice as much as both first and second. How much has each ?

Ans. First-$66.6663. Second $133.333}. Third $400.00. 10. A bankrupt gives up his whole property $600.00, to his creditors, to whom he stands indebted as follows: to A, $780.00 to B, $460.00, and to C, $760.00. What is each creditor's share?

Ans. A's, $234.00, B's $138.00, C's $228.00.

NOTE. In practice, it is customary to find first how much the bankrupt can pay on a dollar, and in speaking of the amount of the deficiency, it is customaryto say he pays so much on a dollar, or somnctintes so much per cent. Finding what he pays on 1 dollar, and afterwards on a larger debt, is evidently not preportion, but analysis.

11. An insolvent gives up property to the amount of $1,557.50, to be divided among the following creditors; A, to whom he owes $300.00; B, to whom $1,100.00; C, to whom $1,150.00; D, to whom $505.00; E, to whom $25.00; and F, to whom $35.00. At what per ct. does he pay, how much on a dollar, and how much on each debt? Ans. 50 per ct.-50 cts. on a dollar. To A, $150.00; to B, $550.00; to C, $575.00; to D, $252.50; to E, 12.50, and to F,$17.50.

12. A certain rich man left $243,000 to be distributed among 7 children, of the following ages, 3, 5, 7, 9, 11, 13 and 15 years re

spectively. The third and fifth are sons, the rest daughters. They are to share in the ratio of their ages, except that the males are to share in twice as great a ratio as their ages would allow. What is the share of each? Ans. The shares arranged in the same order are, $9,000 $15,000 $42,000 $27,000 $66,000 $39,000 $45,000.

13. Frederick, William, Thomas and Henry were to share an estate of $54,000 in the ratio of the numbers of the letters in their first How much had each? Ans. Frederick, $18,000; William, $14,000; Thomas, $12,000"; Henry, $10,000.

names.

14. But it was proved in court, that Frederick used to spell his name without a K. So his share was diminished, and the others increased. How much did he lose by spelling his name without a K, and how much did the others gain?

Ans. Frederick lost $1,384.615; William gained $538.4617; Thomas gained $461.5381; and Henry gained $384.615.

pro

A TAX is a sum of money required of individuals by a government, for the use of the nation; or by a town, county, society, or corporation, for the purpose of defraying the expenses of the whole, in their collective capacity. A tax is sometimes imposed by government, of a small sum upon every male citizen above a certain age, and this being the same to all, and not varying with the amount of an individual's property, is called, a tax of so much a head, or, of so much a poll; the word poll, meaning head. This is commonly abbreviated into the more concise expression POLL-TAX. In some States no poll-tax is allowed. Other taxes are usually rated or assessed on property. Property is of two kinds, real and personal. Real property, or, as it is usually called, real estate, consists of possessions, which are fixed and immoveable; as lands and buildings. Personal perty, comprehends all other possessions, which, of course, are moveables; as furniture, jewels, money, cattle, &c. Taxes are assessed on property, both real and personal. When, therefore, no particular kind of property is mentioned, property generally, or, of all kinds, is understood. In order to assess a tax of this kind, then, or, in other words, to apportion or rate it justly among the individuals of a town or society, we must have a list, or inventory of all the property, both real and personal, on which it is to be assessed. If there is likewise à polltax included in the whole amount given, we must also have the whole number of polls, or rateable heads, or persons. We must then find the amount of all the poll-taxes, or the whole poll-tax, which we must subtract from the whole given tax, and the remainder is to be assessed on property. It is the most expeditious method of making this assessment, to find the taxes on $1.00, $2.00, $3.00, &c., up to $9.00. Then the taxes on $10.00, $20.00, $30.00, &c., up to $90.00

Then

on $100.00, $200.00, &c., up to $1,000.00, and if the town or society be very wealthy, on $2,000.00, $3,000.00, &c., up to $10,000.00. Arrange these taxes in a table, and then from the inventory, knowing each one's property, his tax may be taken out of the table, without the trouble of calculation. It is convenient, likewise, to arrange the polls, from 1 to 10, on one side of the table. This is obviously an analytic process, as, in fact, are most of the practical operations of men of business. We will illustrate this method.

15. A town valued, by inventory, at $97,595.50, raises a tax of $4,155.82. There are 630 polls, and the individual poll-tax is $0.40. Find the tax on a dollar, and form a table as above directed. 630.40 $252.00, amount of poll-taxes. Hence, $4,155.82-$252.00 $3,903.82 is to be assessed on property.

tax on $1.00. From this we easily form the

390382-04 9759550.

1 $0.40 $1.00 $0.04 $10.00 $0.40 $100.00 $4.00 $1,000.00 $40.00

1.20

3. "

0.12

30."

1.60

4. "

0.16

40.

2.00

5. "

4,000. "

0.20

160. "

50. "

5,000."

200. "

80. " 3.20
90."

3.60 900." 36,"

9,000." 360."

10,000.

400."

16. From this table, find the taxes on the following persons. A, property, $7,000.00 real, $800.00 personal; pays for 3 polls: B, property, $9,000.00 real, $7,00.00 personal; pays for 4 polls: C, property, $6,000.00 real, $900.00 personal; pays for 1 poll: and D, property, $15,000.00 real, $1,100.00 personal; pays for 6 polls. A's whole property=$7,800. Tax on $7,000.00

In like manner, B's $389.60; C's $276.40; and D's $646.40. 17. Assess the tax on the following persons, by the last table. E, whole property, $900.00, pays for 2 polls; F, $800.00, pays for 1 poll; G, $750.00, pays for 3 polls; H, $323.50, pays for 1 poll; I, $270.25, 2 polls; J. $300.75, 2 polls; K, 8175.25, 1 poll; L, $643.00, 1 poll; M, 8471.50, 2 polls; N, 8833.75, 3 polls; 0, $543. 75, 2 polls; and P, $975.00, 4 polls.

18. A town is valued at $298,769.50, and is taxed $6,177.89. There are 675 polls, taxed $0.30 each. What is the tax on a dollar? Ans. $0.02 on $1.00.

19. Form a table from the last example, and find the taxes of the following persons. A, property, $3,125.75, 2 polls; B, $936.00, polls; C, $540.00, polls; D, $900.00, 3 polls; E, $1,500.25, 3 polls; F, $763.00, 4 polls; G, $300.00, 3 polls; H, $984.00, 3 polls; I, $1,700.00, 4 polls; J, $1,125.25, 6 polls; K, $727.50, 5 polls; and L, $1,384.00, 5 polls.

COMPOUND PROPORTION.

MENTAL EXERCISES.

§ XCIII. 1. If 2 men can mow 16 acres in 4 days, how many acrés can 5 met mow in 3 days?

2. If 2 barrels of provisions will last 2 persons 4 months, how long will 5 barrels last 9 persons?

3. If a man can travel 72 miles in 6 days, travelling 6 hours a day, how far can he travel in 8 days, travelling 2 miles a day.

4. If a man can shingle 5 houses in 5 months, labouring 10 hours a day, how many houses can he shingle in 2 months, labouring 15 hours a day?

5. If 3 men build 12 rods of wall in 5 days, how many men will be able to build 16 rods in 2 days?

6. If 7 men dig 21 rods of a ditch in 3 days, how many men will it take to dig 27 rods in 9 days?

7. If a box of a certain depth, and 4 ft. long and 3 ft. wide, contain 24 pecks, how long must a box of the same depth, and 4 ft. wide be, to contain 40 pecks?

8. If it take 3 yards of cloth that is 7 quarters wide to make a suit, how much that is 3 quarters wide will it take to line it?

9. If 5 men can do a piece of work in 8 days, working 5 hours a day, how many hours a day must 10 men work, to do it in 10 days? Let the following be written.

10. If 20 laborers will clear 60 acres of woodland in 2 months, how many acres will 35 laborers clear in 6 months?

ANALYTIC SOLUTION. If 20 men clear 60 acres, man, in the same time, will clear as much=&g=3 acres. If he clear 3 acres in 2 months, he will clear as much in 1 month= acres. 35 men would clear 35 times as much in a month=35X3=195, and in 6 months, they would clear 6 times as much=6×195630315 acres, Ans.

By proportion, the process is as follows:

It will be observed, that the answer is affected, both by the number of the men, and by the length of time they work. Suppose we find what the answer would be supposing they worked the same length of time, that is 2 months, in each case. The number of men will, then, be the only circumstance on which the answer depends, and the question becomes one of Simple Proportion, stated thus,

20 : 35 :: 60 : ***60×35÷20-105 acres. It seems, then, that the 35 men will clear 105 acres, while the 20 are clearing 60 acres. But they have, likewise, more time to work in, and the question now is, if they will clear 105 acres in 2 months, what will they clear in 6 months; stated thus,

months months acres acres

2.

6 ::

105 : *****=105X6+2=315 acres.