*3. A man being determined to mix 12 bushels of oats at 18d per bushel, with barley at 2s 6d. with rye at 3s. and with wheat at 4s. per bushel-I demand how much barley, rye and wheat must be mixed with the 12 bushels of oats, that the whole may bear the price of 2s 9d per bushel.

7 Answer, 12 bushels of each sort.

4. A man being dstermined to mix 12 bushels of oats, at 18d per bushel, with barley at 2s. 6d. with rye at 3s. and with wheat at 4s per bushel-I demand how much barley, rye and wheat must be mixed with the 12 bushels of oats, that the whole quantity may bear the price of 38 6d per bushel ?

Ans.

{

B.

12 of Barley
12 of Rye
84 of Wheat

5. A man intends to mix 28 bushels of oats, at 18d per bushel, with barley at 2s. 6d. with rye at 3s. and with wheat at 4s. I would know how much barley, rye and wheat ought to be added to the 28 bushels of oats, that the whole quantity may be afforded at 28. per bushel? Answer, 4 bushels of each sort.

6. A Farmer would mix 27 bushels of peas, at 18d per bushel, with oats at 284. and with beans at 30d. per bushel, that the whole quantity may bear the price of 20d per bushel-I demand how much oats and beans must be mixed with the 27 bushels of peas? Answer S bushels of each sort.

K

CASE 3.

OF ALTERNATION TOTAL.

Q. What do you observe in this third case?

A. When the rates of the several things, the quantity to be compounded, and the mean rate of the whole mixture are given, to find how much of each sort will make up the quantity; place the differences between the several prices, and the mean rate, alternately, as in case 1, then say, As the sum of the differences,

Is to the whole composition:

So is the difference of each rate,

To the quantity of the same rate.

EXAMPLES.

1. A grocer had 4 sorts of sugar, viz. at 8d per lb. at 6d. at 4d and at 2d. per lb. and he would have a composition of an Cwt. worth 5d per lb. I demand how much of each sort he must take?

2. A. Vintner hath 4 sorts of Wine, viz. Canary at 10s. per gallon, Malaga at 8s. Rhenish at 6s. and Oporto at 4s.

and he is minded to make a Composition of 60 gallons, worth 9s. per gallon-I demand how much of each sort he must have? Ans. 45 gallons of Canary, aud 5 gals. of each other sort.

3. A Brewer hath 3 sorts of ale, to wit, at 10d. at 8d. and at 6d. per gallon-and he would have a composition of 30 gallons, worth 7d. per gallon-I demand how much of each sort he must have? Gals. d.p.gal.

4. A Goldsmith hath several sorts of Gold, viz. some of 24 carrats fine, some at 22 carrats, and some of 18 carrats fine; and he would have compounded of these sorts the quantity of 60 oz. 20 carrats fine-I demand how much of cach sort he must take ?

5. A Goldsmith hath Gold of 3 sorts, viz. of 22 carrats, of 21 carrats, and of 20 carrats fine, and he would mix with these so much Alloy, as that the quantity of 21 oz. may bear 18 carrats fine, I demand how much of each sort he must take, and how much alloy? Ans. 6 oz. of each sort of Gold, and 3 oz. of Alloy.

6. A Druggist had 3 sorts of Drugs, one was worth 4s per lb. another 5s and another 8s. and out of these he made two parcels, one was 21lb. at 6s. per lb. and the other 35 lb at 7s. per lb. how much of every sort did he take for each parcel?

lb. sp.lb.

6 at 4
6 at 5

lb s.p.lb.

5 at 4

5 at 5

25 at 8

21 at 6s p. lb. 35 at 7s p. lb.

Q.

OF POSITION.

WHAT is Position; or Negative Arithmetic ?

A. It discovers the Truth by supposed Numbers.
Q. How many Kinds of Position are there?
A. Two; Single and Double.

OF SINGLE PUSITION.

Q. What is Single Position?

A. It discovers the truth by only one supposed number, Q. How is that supposed number used ?

A. By working with it, as if it was the true number, in the same proportion as the question directs; and if the result be either too much or too little, the true number may be found out by the following Rule, viz.

As the Result of the Position,

Is to the Position:

So is the given Number,

To the number required.

Q. How do you prove Position?

A. Position, both Single and Double, is proved by adding the several sums required, or the several parts of the sum required, together; and if that sum agrees with the given sum, it is right.

EXAMPLES.

1. Two men, A and B, having found a Bag of Money, disputed who should have it; A said the half third and fourth of the money made 130l. and if B could tell how much was in it, he should have it all, otherwise he should have nothing? I demand how much was in the bag?

Ans. 1201.

2. A, B and C, determined to buy together a certain quantity of timber, worth 361. agree that B shall pay more than A, and C more than B-I demand how much each man must pay? Ans. A. 91. B 121. C 15l.

3. A person having about him a certain number of Crowns, said if the half, third and fourth of them were added together, they would make 65 Crowns-I demand how many he had? Ans. 60 Crowns.

4. Clent Da sum of money, to be paid at 4 payments; when three of them were made, and C came to demand the fourth, D would give him no more, except he would tell him how much was paid already: C said the first payment was a fourth, the second a fifth, and the third a sixth of the sum first lent, and altogether made 747. I demand the sum lent? Ans. 1207.

5. One man carrying a bag of money in his hand, another asked him how much was in it; he answered, he could not tell: but the third, fourth, and fifth of it made 941. How much was in the bag? Answer 110l.

6. I have delivered to a Banker a certain sum of money, to receive of him after the rate of 61. per cent. per annum; and at the end of ten years he paid me 500 for Principal and Interest together; I demand the sum delivered to him at first? Answer 312/ 10s.

OF DOUBLE POSITION.

Q. What is Double Position?

A. It is that which discovers the true number sought, by making use of two supposed numbers.

Q. How are those supposed numbers used?

A. 1. By working with them as if they were the true numbers in the same proportion as the question directs. 2. The result or Errors must be placed against Pos.Er. their Positions, or supposed Numbers thus,

3. Multiply them Cross-wise.

40 28

36 19

4. If the Errors are alike, i. e. both greater, or both less than the given number, take their difference for a divisor, and the difference of the products for a dividend.

5. If the Errors are unlike, take their sum for a divisor, and the sum of the products for a dividend; the quotient thence arising will be the answer.

EXAMPLES.

1. B, C and D, would divide 100/ between them, so as that C may have 31 more than B, and D 41 more than C: I demand how much each man must have? Answ. B 30l. C 331. D 371.

2. A man lying at the point of death, said he had in a certain coffer 100l which he bequeathed to 3 of his friends after this manner: the first must have a certain portion, the second must have twice as much as the first, wanting 8. and the third must have three times as much as the first, wanting 15l. I demand how much each man must have? Answer, the first 20l. 10s. second 331. third 46l. 10s.

3. B, C and D built an House which cost 1007. of which B paid a certain sum, C paid 10l. more than B, and D paid as much as B and C-I demand each man's share in that charge? Ans. B 201. C 301. D 501.

4 Three persons discoursed together concerning their ages; says B, I am 20 years of age; says C, I am as old as. B, and half D; and says D, I am as old as you both; I