pany, $200; A's stock was $150, B's $250, and C's $400. what was the gain on $1, and what was each man's share of the gain. A. The gain on $1 is $4; then, 4 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 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 $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 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 $1800 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 company, with a joint capital of $1000; they gained $400, of which A took $300, and B the remainder; what was each person's stock? Ans. $1 gain requires 25 stock; A's, $750; B's, $250. 8. Divide $1000 between 4 persons, so that their shares may 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 E $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, is the general practice to find how much the debtor pays on $1, which is, in this case, Ans. A, $175; B, $500; C, $600; D, $210; E, $42,50; F, $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 tax 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: polls C's, at 1200, pays for 2 D's, 1265, F's, 3621, $ cts. polls. H's, at 825,50, pays for 3 1 I's, 2 3 J's, 375,25, ..... 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 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 × $,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 F's? (14624) What H's? (3512) What I's? (334160) What J's? (1571) What K's? (12012) Ans. $430,298 COMPOUND FELLOWSHIP. ¶ 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 × 6=) 12 oxen for 1 month; and 3 oxen for 5 months is the same as (3 × 5 =) 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 3X5=1527:12:: 9: $4, A's. 27 Q. How, then, does Compound differ from Simple Fellowship? pound regards time, Simple does not. Q. From the preceding example, what appears to be the RULE ? A. Com 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: each 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 they lose $50: how much loss must each man sustain ? Ans. A's, $7,058+ A puts in 80 sheep sheep for 5 mo.; A's, $19,20, 3. Three butchers hire a pasture for $48: for 4 mo., B 60 sheep for 2 mò., and C 72 what share of the rent must each man pay? Ans. B's, $7,20, 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 the expiration of 6 months, took out $250; with this stock they A's, $200,797, gained $386; what was each 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 each man's share of the gain? Ans. A's share, $384,929; B's, $250,71; C's, $236,36, Q. What are your ideas of a square? 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 ap pear to be? A. A square figure. 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. A. Angles. Q. How, then, would you describe a square figure? equal sides, and four equal angles. B D Q. In the above figure, if each side be 1 foot in length, what ought it to be called? A. 1 square foot. Q. If the sides of a square be each 1 yard in length, as in the figure on the right, what ought it to be called? A. 1 square yard. Q. In this square I perceive there are several smaller squares, contained in the larger. If you count all the smaller squares, allowing each one to 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 foot, that is, 1 square yard. 3 feet 1 yard. A 3 feet1 yard. B D Q. How many square feet, then, make 1 square yard? A. 9. Q. If we multiply 3 feet (the length of 1 side) by the width, 3 feet, making 9, the same result is produced as before. What, then, will multiplying the length of any square by the breadth, or the length into itself, give? square feet, square inches, &c., contained in the figure. A. The Q. How many square inches in a figure 2 inches long and 2 inches wide? 2 × 2=4, Ans. How many 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? 20 inches square? 30 inches square? Q. How many square feet in a figure 1 foot, or 12 inches, square? A. 1 square foot. Q. How many square inches in 1 square foot? and why? A. 144. sq. in., because 12 in. x 12 in. 144. Q. How many square feet in 1 square yard? and why? A. 9 sq. ft.; because 3 ft. x 3 ft.: = 9 Q. How many square yards in 1 square rod? and why? A. 304 sq. yds., because 5 yds. × 5 yds. 30 Q. How many square feet in 1 square rod? and why? A. 2724 sq. ft., because 16 ft. (the number of feet in 1 rod in length) × 16 ft. =2721. A Q. This figure on the right is called a parallelogram: what, then, are your ideas of a parallelogram? A. That it is a figure, which is longer than it is wide. F B E C Q. We see by this figure, that there are two kinds of parallelograms, viz. ABCD and ABEF. By inspecting these they will be found to be equal: how, then, may a parallelogram be defined? A. It is a figure which has its opposite sides of equal length, and its opposite angles equal. Q. If this figure 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 feet, and the shortest side only 1 foot, it will, of course, contain but as many square feet. How many, then, does it contain? A. 2ft. (length) × 1 ft. (breadth) = 2 sq. ft. Q. If a figure 1 inch in breadth and 1 inch in length contains 1 square inch, how 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 feet long? 10 feet long? Q. How, then, do you proceed to find the square feet, 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 feet 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? 11 rods long? 12 rods long? 10 rods long and 4 rods wide? Q. When a piece of land, in any shape, contains 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 wide? 4 rods wide? Q. When a piece of land, in any shape, contains 160 square rods, what is it called? A. 1 acre. 4. How many square rods in a piece of land 20 rods long, and 2 rods wide? How many such pieces will make an acre, or 160 square rods? 5. How wide must 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 feet square? 10 feet wide and 20 feet long? 20 feet wide and 30 feet long? |