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Many, $200; A's stock was $150, B's $230, and C's $400. what was the gain on $1, and what was cach man's share of the gain. A. The gain on $1 is $; then, of $150 = $37,50 A's; of $250= $02,50, B's; and 4 of $400 $100, C's.

3. A, B, and C, freight a ship with 270"tons ; Å slipped on board 96 tons, B 72, and C 102; in a storm, the scamcn wero obliged to throw 90 tons overboard · what was the loss on 1 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 $500; A put in $350,50, and B $249,50, and, by trading, they gained $130 : what is the gain on $1, and what is each person's shars of the gain? Ans. $$ ; A's, $70,10; B's, $49,90.

5. A ship valued at $25200, was lost at sea, of which f be. longed to A, } to B, and the remainder to C; what is the loss on $1, and how much will each man sustain, supposing $180C. 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 coinpanios, was sent into a garrison, in which the duty required 228 mon a day; the first company consisted of 102 men; the second, 153; the third, 144; the fourth, 11?; and the fifth, 108 ; how many men must each company furnish, in proportion to the whole number of men ? A. The proportion for 1 an 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 company, with a joint capi: tal of $1000; they gained $400, of which A took $300, and B the remainder; what was each person's stock? Ans. $1 gaix requires 25 stock; A's, $750; B's, $250.

8. Divide $1000 between 4 persons, so that their shares may oe to each other as 1, 2, 3, 4. 4. $100, $200, $300, $400.

9. A bankrupt is indebted to A $350, to B $1000, to $1200, to D $420, to E $85, to F $10, 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 practica to find how much tho debtor pays on $1, which is, in this case,

Ans. A, $175; B, $500; C, $C00; D, $210; E, $42,50 ; F, $20; G, $10.

10 A wealthy merchant, at his death, left an estate of $39000, to be divided among his 5 children, in such a manner that their shares shall be to each other as their ages, which 7e 7, 10, 12, 15, 16 years; what was the share of each

Ans. $3500, $5000, $6000, $7500/48000

11. A and B invest equal sums in trade, and clear $220, of which A is to have 8 shares, because lie 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 laxed; and, as the whole number of polls arc rated at so much each, the tax on all the polls must first be taken out from the while tax, and the remainder is to be assessed oa the property. Then, to find how much any individual must bo 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 po!l 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 polis. polls

polls. C's, at 1200, pays for 2 H's, at 825,50, pays for 3 D's, ... 1265,

1 I's,
800,40, .......

2
E's,
2125,

3
J's, 375,25,

1
F's,
3621,
K's, ... 265,30,

2 What will be the tax on $1 ? and what will be A's tax ? 200 polls * $,70= $140, amount of the poll taxes, and $2140 $140 $2000, which is to be asscssed 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
polls at $,70 1,40

$57,40 A's whole tar, Ans. What will be C's tax? (4940) What D's? (5130) What E's? (8710) What F's? (14624) What H’s? (3512) What I's? 7334160) What J's ? (1571) What K's? (12012)

Ans. $430,298

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......

COMPOUND FELLOWSHIP. 1 LXXVIII. 1. Two men hired a pasture for $9; A put in 2 oxon for 6 months, and B 3 oxen for 5 months; what ought eaub to pay for the pasluro?

2 oren for 6 months is the same as (2 ; 6=) 12 oren for ! month; and 3 oxen for 5 months is the same as (3 x 5=) 15 ozen 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,

2x6 =12

1:27: 12: :9: $4, A's. 3x5=15

27 | 27: 15::9: $5, B's. Q. How, then, dves Compound differ from Simple Felloroship?

A. Com pound regards time, Simple does not. Q. From the preceding example, what appears to be the

Role? I. Multiply each man's stock by the time it is continued in trade.

II. Then-As the sum of the products : each man's product : : the whole gain or loss : cach man's gain or loss.

More 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 thoy lose $50 : how much loss inust each man sustain ?

A's, $7,0587. Ans. B's, $14,7054

C's, $28,2357 3. Three butchers hire a pasture for $48: A puts in 80 sheep for 4 mo., B 60 sheep for 2 mo., and C 72 shcep for 5 mo., what share of the rent must each man pay? À's, $19,20,

Ans. B's, $ 7,20,

C's, $21,60. 4. Two merchants entered into partnership for 16 mo.: A at first put in stock to the amount of $600, and, at the end of 9 months, put in $100 more; B put in at first $750, and, at tho oxpiration of 6 months, took out $250; with this stock they gained $386; w.jat was cach man's part?

Ans. :

B's, $185,202. 5. On the first of January, A began trade with $760, and, on the first of February following, he took in B with $540 ; on the first of June following, he took in C with $800 ; at the end of the year they found they had gained $872; what was cach man's share of the gain?

Ans. A's share, $384,929 ; B's, $250,71 ; C's, $236,36

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What are your ideas of a squaro ? A. It is A any thing which is as long as it is wide.

Q. What kind of a figure does this on the right appar to be? A. A square figuro.

Q. Why? A. Because the side AB is as long as the side BC.

Q. How many sides has this figure, and what is their length ?

Q. How many equal corners has it? A. Four. Q. What are these corners generally called ? A. Angles.

D

C Q. How, then, would you describe a square figure ?

A. It has fc equal sides, and four equal angles.

Q In the above figure, if each side be I foot in length, what ought il te called? d. I square foot.

A 3 foet =lyard. B Q. If the sides of a square bc each 1 yard in length, as in the figure on the right, what ought it to be called ? A. square yard.

Q. In this square I perceive there are several smaller syuares, contained in the larger. If you count all the smaller squares, allowing each one to 11 be 1 foot, how many square feet or square yards will they make ?

Q. Why? A. Because there are 9 small squares, each containing 1 square foot, which make 9 square feoi, that is, 1 squaro

D j'ard.

Q. How many square feet, then, make 1 square yard? A. 9.

2. If we multiply I Feet (the length of 1 side) by the width, 3 feet, making 9, the same result is produced as before. What, then, will multipiying the length of any square by ere breadth, or the length into itself, give ? A. Tlie square feet, square ii ches, &c., contained in the figure.

Q. How many square in:hes in a figure 2 inches long and 2 inches wide ; 2 X 2=4, Ans.

Hou muny in a figure 4 inches long and 4 inches wide ! 12 inches square, that is, 12 inches long, and 12 inches wide ? 8 inches square 6 inches square 1 20 inches square? 30 inches squarc?

Q How many square feet in <figure 1 foot, or 12 inches, square ? A. I square fool.

(I. Houd many squarc inchcs in 1 square foo!? and why? A. 144. s7 in. because 12 in. X 12 in. = 144.

Q. How many square feet in 1 square yard ! and ung? A. 9 sq. ft. because 3 it. X 3 tt

2. Ilow many equare yards in 1 square roar une sohy? f. 307 sq. yos. becauso 5vis. X 50 yds.=300

3 feet =lyard

Q: How many square feet in 1 square rod? and why? A. 2724 sq. ft. because 164 ft. (the number of feet in 1 rod in length) x 164 it = 272,1

B Q. This figure on the right is called a parallelogran : what, then, are your ideas of a parallelogram? A. That it is a figure, which is longer than it is wide. F D

E Q. We see by this figure, that there are two kinds of parallelograms, riz ABCD and ABEF. By inspecting these they will oe found lo be equal : how, then, måy a parallelogram be defined ? A. It is a figure which has its opposite sides of equal length, and its opposite angles equat,

Q. If this figlire had been square, and each side 2 feet in length. it is plain that it would have contained 4 square feet ; but, allowing the longest side to be 2 fect, and the shortest side only 1 foot, it will, of course, contain but į as many square feet.- How many, then, does it contain ? A. 2 A. (lòngth) x 1 ft. (breadth) = 2 sq. ft.

Q. If a figure 1 erich in breadth and 1 inch in length contains 1 square ini h kuro many square inches will a figure 1 inch wide and 2 inches long contain ? 3 inches long? 4 inches long ? °8 inches long? 12 inches long? 20 inches long?

Q. If a figure 1 foot wide and 1 foot long contains 1 square foot, how many square feet will a figure 1 foot wide and 2 feet long contain? 3 feet long 4 feet long? 8 fect leng? 10 feet long?

Q. Horo, then, do you proceed to find the square fect, inches, &c. of a square or parallelogram? A. Multiply the length by the breadth.

1. How many square feet in a room 10 feet long and 2 foet wide ? (10 X 2=20 sq. ft., Ans.) In a room 8 feet wide and 12 feet long? 20 feet long?

2. How many square rods in a piece of land 4 rods wide and 8 rods long ? *10 rods long? 1l rods long?

12 rods long? 10 rods long and 4 rods wide ?

Q. When a piece of land, in any shape, contams 40 square rods, what is it called ? .A. 1 rood.

3. How many square rods in a piece of land 40 rods long and 2 rods wid: ? 4 rods wide ?

Q. When a piec! of land, in any shape, contains 160 squarc rods, what is it sallcd ?

A. 1 a're. 4. How many square rods in a piece of land 20 rods long, and 2 rods wid? How many such pieces will make an acre or 160 square vods?

5. How wida qust a piece of land be, which is 80 rods long to make an acre 40 rods long? 20 rods long?

6. How many square feet of boards are contained in the floor of a room 10 feet square? 20 fect square? 10 feet wide and 20 feet long? 20 feet wide and 30 feet long

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