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Note. Give one of them 7, and then divide the rest equally.
125. A gentleman divided an estate of $15000 between his two sons, giving the elder $2500 more than the younger. What was the share of each ?
126. A gentleman bequeathed an estate of $50000, to his wife, son, and daughter; to his wife he gave $1500 more than to the son, and to the son $3500 more than to the daughter. What was the share of each ?
127. A, B, and C, built a house, which cost $35000; A paid $500 more, and C $300 less than B. What did each pay
128. A man bought a sheep, a cow, and an ox, for $62; for the cow he gave $10 more than for the sheep; and for the ox $10 more than for both. What did he give for each ? 129. A man sold some calves and some sheep for $108; the calves at $5, and the sheep at $8 apiece. There were twice as many calves as sheep. What was the number of each sort?
Note. There were two calves and one sheep for every $18.
130. A farmer drove to market some oxen, some cows, and some sheep, which he sold for $749; the oxen at $28, the cows at nike fractionat $7.50. There were twice as many cows as oxen, and three times as many sheep as Cows. How many were there of each sort?
131. A man sold 16 bushels of rye, and 12 bushels of wheat for £8. 16s. The wheat at 3s. per bushel more than the rye. What was each per bushel ? Note. The whole of the wheat the same number of bushels of rye. remainder will be the price of 28 bushels of rye.
came to 36s. more than Take out 36s., and the
132. Four men, A, B, C, and D, bought an ox for $50, which they agreed to share as follows: A and B were to have the hind quarters, C and D the fore quarters. The hind quarters were considered worth cent per lb. more than the fore quarters. A's quarter weighed 217 lb.; B's 223 lb.; C's 214 lb.; and D's 219 lb. The tallow weighed 73 lb., which they sold at 8 cents per lb. ; and the hide 43 lb., which they sold at 5 cents per lb. What ought cach to pay?
133. At the time they bought the above ox, the fore quarters of beef were worth 6 cents per lb., and the hind quarters 6 cents per lb. It is required to find what each ought to pay in this proportion.
Note. This is a more just manner of dividing the cost, than that in the last example. It may be done by finding what the quarters would come to, at this rate, and then dividing the real cost in that proportion.
134. Said A to B, my horse and saddle together are worth $150, but my horse is worth 9 times as much as the saddle. What was the value of each?
135. A man driving some sheep and some cattle, being asked how many he had of each sort, said he had 174 in the whole, and there were as many cattle as sheep. Required the number of each sort.
136. A man driving some sheep, and some cows, and some oxen, being asked how many he had of each sort, answered, that he had twice as many sheep as cows, and three times as many cows as oxen; and that the whole number was 80. Required the number of each sort.
137. A gentleman left an estate of $13000 to his four sons, in such a manner, that the third was to have once and one as much as the fourth, the second was to have as much as the third and fourth, and the first was to have as much as the other three. W was the share each? 138. A, B, and C playing 324 crowns; but disputing about the tricks, each man took as many crowns as he could get. A got a certain number; B as many as A, and 15 more; and C part of both their sums added together. How many did each get?
139. The stock of a cotton manufactory is divided into 32 shares, and owned equally by 8 persons, A, B, C, &c. A sells 3 of his shares to a ninth person, who thus becomes a member of the company, and B sells 2 of his shares to the company, who pay for them from the public stock. After this, A wishes to dispose of the remainder of his part. What proportion of the whole stock does he own?
140. Three persons, A, B, and C, traded in company. A put in $75; B $40; and C a sum unknown. They gained $64, of which C took $18 for his share. What did C put
141. How many cubic feet in a cistern, 4 ft. 2 in. long, 3 ft. 8 in. wide, and 2 ft. 7 in. high?
A method of doing this by decimals has already been shown. It is now proposed to do it by a method called duodecimals.
First, I find the square feet in the bottom of the cistern. 3 ft. 8 in. 3 ft. 4 ft.
4 ft. 2 in.
2 ft. 7 in. 27 ft.
15,4 square feet in the bottom.
Ans. 39++ cubic feet in the cistern.
is, I write down the 4 then of 4 is 32 and (which was 22, which I write down. Then 3 times is, and 3 times 4 are 12. These added together make 15+ square feet. Then to find the cubic feet, I multiply this by 25 is 748=144 +1728, I write the 8, and reserve the 44; then 1 of 12 is 144 and (which were reserved) are 144 11⁄2 +14; I write down the and reserve the then 7 of 15 are 87/2 and (which was reserved) is 819. 2 times are 144; and 2 times are and 2 times 15 are 30. Adding them together, and are =+; I write the, and reserve the; then 12 and are 15, and 12 (which was reserved) is 1. The whole is 39 11 17--7728°
S we know that 12ths multiplied by 12ths will pro duce 144ths, and that make; and, also, that 144ths multiplied by 12ths produce 1728ths, and that make 14, we may write the fractions without their denominators, if we make some mark to distinguish one from the other. It is usual to distinguish 12ths by an accent, thus ('), 144ths thus ("), 1728ths thus (""), &c. 12ths are called primes. 144ths seconds; 1728ths thirds, &c.
Cubic feet 39 5' 77 4
The operation is precisely the same as before. To adopt the language suited to this notation, we say, units multiplied by primes or primes by units produce primes, seconds by units produce seconds, &c. primes by primes produce seconds, seconds by primes produce thirds. Also 12 thirds make 1 second, 12 seconds 1 prime, 12 primes make 1 foot, whether long, square, or cubic. The same principle extends to fourths, fifths, &c.
142. How much wood in a load 4 ft. 8 in. high, 3 ft. 11 in. broad, and 8 ft. long?
Note. Multiply the height ar breadth together, and divide by 2. See page 102.
143. How many square feet in a floor 16 ft. 8 in. wide, and 18 ft. 5 in. long?
144. How much wood in a pile 4 ft. wide, 3 ft. 8 in. high, and 23 ft. 7 in. long?
145. If 11 barrels of cider will buy 4 barrels of flour, and 7 barrels of flour will buy 40 barrels of apples; what will 1 barrel of apples be worth, when cider is $2.50 per barrel ?
146. A person buys 12 apples and 6 pears for 17 cents, and afterwards 3 apples and 12 pears for 20 cents. What is the price of an apple and of a pear ?
Note. At the second time he bought 3 apples and 12 pears for 20 cents, 4 times all this will make 12 apples and 48 pears for 80 cents; the price of 12 ap les and 6 pears being taken from this, will leave 63 cents for 42 pears, which is cent apicce
147. Two persons talking of their ages, one says of mine is equal to of yours, and the difference of our ages is 10 years. What were their ages?
148. A gentleman divided some money among 4 persons, giving the first as much as the second and fourth; the second as much as the third and fourth; the third, half as much as the first; and the fourth, 5 cents. How much did he give to each ?
149. Two persons, A and B, talking of their ages, A says to B, of mine and of yours are equal to 13; B says to A, of mine and of yours are equal to 16. What was the age of each?
150. A person drew two prizes; of the first, and of the second was $120; and the sum of the two was $400. What was each prize?
151. Two persons purchase a house for $4200; the first could pay for the whole, if the second would give him of 13 his money; and the second could pay for the whole, if the first would give him of his money. How much money had each.
152. A man bought some lemons at 2 cents each, and 2 as many, at 3 cents each, and then sold them all at the rate of 5 cents for 2, and by so doing gained 25 cents. How many lemons did he buy?
153. These are two cisterns which receive the same quantity of water; the first nstantly loses of what it receives; after running 7 days, 10 barrels were taken from the second, and then the quantity of water in the two was equal. How much water did each receive per day?
154. A man having $100 spent a certain part of it; he afterwards received five times as much as he spent, and then his money was double what it was at first. How much did
155. A man left his estate to 2 sons and 3 daughters, each son had 5 dollars as often as each daughter had 4; the difference between the sum of the sons' shares and that of the daughters, was $1000. Required the share of a son. 156. A man left his estate to his wife, son, and daughter, as follows to his wife of the whole, and as much as the share of the daughter; to his son of the whole, and to the daughter the remainder, which was $1000 less than the share of the son. What was the share of each?
'57. A man bought some oranges for 25 cents; if he had