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 1 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 $17, and the sheep at $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 came to 36s. more than the same number of bushels of rye. Take out 36s., and the remainder will be the price of 28 bushels of rye.

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 lbs.; B's 223 lbs.; C's 214 lbs.; and D's 219 lbs. The tallow weighed 73 lbs., which they sold at 8 cents. and the hide 43 lbs, which they sold at 5 cents per lb. What ought each to pay ?

per

lb.;

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 20 as many cattle as sheep. Required the number of each sort.

9

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 half 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. What was the share of each?

138. A, B, and C playing at cards, staked 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 in?

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.

Ans. 3912 +7 +172 cubic feet in the cistern.

I say

16 ofis

4

of is = 12 +7, I write down the 12 and reserve the

2

2

7

ΤΣ

23

4

4

1

3

4

8 ΤΣ

4

2

144

12

then of 4 is 32 and (which was reserved) is 2, 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 2. of T 7 4/1 is 1728 = 144 + 772, I write the 7725, and reserve the then of 12 is, and (which were reserved) are = 12 + 1; I write down the and reserve the; then 7 of 15 are 8 and 72 (which was reserved) is 819. 2 times are t and 2 times are, and 2 times 15 are 30. Adding them together, and are 8 Tare = i +r; 1 write the, and reserve the ; then 19 10 and 12 are 19, and (which was reserved) is 11. The whole is 39+ T33 + 1728.

747

Since we know that 12ths multiplied by 12ths will produce 144ths, and that 12 make; and, also, that 144ths multiplied by 12ths produce 1728ths, and that make, 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 (''), 1728th_thus (") &c. 12ths are called primes; 144ths seconds; 1728ths thirds, &c.

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 and breadth together and divide by 2. See page 108.

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 apples and 6 pears being taken from this, will leaves 63 cents for 42 pears, which is 1 cent apiece.

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 of mine and

A says to B,

B says to A,

of mine and

What was the age of each?

B, talking of their ages,
of yours are equal to 13; ..
of yours are equal to 16.

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 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 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. There are two cisterns which receive the same quantity of water; the first constantly 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?