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3. A grocer would mix 12 cwt. of sugar at 10 dols. per cwt, with 3 cwt. at 8} dols. per cwt. and 8 cwt. at 71 dols. per cwt. what will 5 cwt. of this mixture be worth ?

Aní,

44 dois. 78 cts. 2 mills. 4. A refiner melts 2{ lb. of gold, of 20 carats fine, with 4

Ib. of 18 carats fine ; how much alloy must he put to it, to make it 22 carats fine ?

Ans. It is not fine enough by 375 carats, so that no

alloy must be put to it, but more gold. 5. A maltfter mingles 30 quarters of brown malt, at 285. per quarter, with 46 quarters of pale, at 30s. per quarter, and 24 quarters of high dried ditto, at 255. per quarter ; what is the value of 8 bushels of this mixture ?

Anf. £.1 8s. 2 d.} 6. If I mix 27 bushels of wheat, at 55. 6d, the bushel, with the Same quantity of rye, at 45. per bushel, and 14 bushels of barley, at 25. 8d. per bushel, what is the worth of a bushel of this mixture ?

Anf. 45. 3d.it 7.

А grocer mingled 3 cwt. of sugar, at 56s. per cwt. 6 cwt. at £:1 17 4 per cwt. and 3 cwt. at £ :3 14 8 per cwt. what is i cwt. of this mixture worth ?

Anf. £.2 11 4 8. A mealman has flour of several forts, and would mix

3

bulho els at 35. 5d. per bushel, 4 bushels at 5s. 6d. per bushel, and 5 bushels at 45. 8d. per bushel, what is the worth of a bushel of this mixture ?

Anf. 45. 7d. Hy is 9. A vintner mixes 20 gallons of Port at 55.4d. per gallon, with I 2 gallons of White wine at 55. per gallon, 30 gallons of Lisbon at 65. per gallon, and 20 gallons of Mountain at 45. 6d. per gallon, what is a gallon of this mixture worth ?

Anf. 55. 3d. 10. A farmer mingled 20 bushels of wheat at 55. per bushel, and 36 bushels of rye at 35. per bushel, with 40 bushels of barley at 25. per bushel, I desire to know the worth of a bushel of this mixture ?

Anf. 3 shillings. A person mixing a quantity of oats at 25. 6d. per bushel, with the like quantity of beans at 45. 6d. per bushel, would be glad to know the value of 1 bushel that mixture ?

Anf. 35. 60. A refiner having 12 lb. of silver bullion of 6 oz. fine, would melt it with 8 lb. of 7 oz. fine, and 10lb. of 8 oz. fane, required the fineness of 1 lb. of that mixture ?

Anf. 6oz. 18 dwt. 16 grs. 13. If with 40 bushels of corn at 45. per bushel, there are mixed 10 bushels at 6s.

per

bushels at 55. per bushel, and 20 bushels at 3s. per bushel, what will 10 bushels of that mixture be worth?

Ans. £.2 35.

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11.

12.

bushel, 30

ALLIGATION ALTERNATE

1.

19

Is the method of finding what quantity of any number of simples, whose rates are given, will compose a mixture of a given rate; so that it is the reverse of Alligation Medial, and may be proved by it.

RULE. 1. Write the rates of the simples in a column under each other.

2. Connect or link with a continued line the rate of each simple which is less than that of the compound, with one, or any number, of those that are greater than the compound, and each greater rate with one or any number of the less.

3. Write the difference between the mixture rate and that of each of the fimples, opposite the rates with which they are linked.

4. Then if only one difference stand against any rate, it will be the quantity belonging to that rate ; but if there be several, their fum will be the quantity,

EXAMPLES. A merchant would mix wines at 145. 195. 155. and 225. per gallon, so as that the mixture may be worth 18s, the gallon ; what quantity of each must be taken?

14

4 at 145. 15

1 at 155. 18

3 at 195.

4 at 225.
Or thus,
14

1+45 145.
18
15

155.
19-

4+37 at 19s.
4 4

at Note. Questions in this rule admit of a great variety of answers, according to the manner of linking them.

How much wine, aţ 6s. per gallon, and at 4 shillings per gallon, must be mixed together, that the composition may be worth 55.

Ans. 1 qt. or 1 gal. &c. 3. How much corn, at 25. 6d. 35.

and
45.
8d. bush.

per el, must be mixed together, that the compound may be worth 3s. 10d.

Ans. 12 at 25. 6d. 12 at 3s. 8d.

18 at 45, and 18 at 45. 8d. 4. A goldsmith has gold of 17, 18, 22, and 24 carats fine; how nuch mußt he take of each to make it 21 carats fine ?

Ans. 3 of 17, 1 of 18, 3 of 22, and 4 of 24. It is required to mix brandy at 8s. wine at 7s. cider at is, and water together, so that the mixture may be worth gs. per gallon ?

Anl. 9 gals, of brandy, 9 of wine, s of cider, and 5 of water.

22

at at

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22

225.

2.

per gallon ?

8d. 45:

per bushel ?

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When the whole composition is limited to a certain quantity, Rule. Find an answer as before by linking; then say, As the sum of the quantities, or differences thus determined, is to the given quantity, so is each ingredient, found by linking, to the required quantity of each

EXAMPLES.

6. How many gallons of water must be mixed with wine worth 35. per gallon, so as to fill a vessel of 100 gallons, and that a gallon may be afforded at 25. 6d. ?

6
30
36

30

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I 2

24

Anf. 834 gallons of wine, and 16 of water. 7. A grocer has currants at 4d. 6d. gd. and 11d. per lb. and he would make a mixture of 240 lb. so that it might be afforded at 8d. per Ib. how much of each fort must he take ?

Ans.

72

lb. at 4d. 24 at 6d. 48 at 9d. and 96 at 11d. 8. How much gold of

15,

of of 18, and of 22 carats fine, muft be mixed together, to form a composition of 40 oz. of 20 carats fine ? Ans. 5 oz. of 15,

of and of 18, and 25 oz. of 22.

17,

17,

When one of the ingredients is limited to a certain quantity. Rule. Take the difference between each price and the mean rate, as before ; then,

As the difference of that simple, whose quantity is given, is to the rest of the differences severally, so is the quantity given, to the sev. eral quantities required,

EXAMPLES. 9. How much wine, at 55. at 55. 6d. and at 6s, the gallon, must be mixed with three gallons, at 45. per gallon, so that the mixture may be worth 55. 4d. per gallon ?

48

8+2=10 607-t

8+2=10
64

66-tt 16+4320
72

16+4=20

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10

:

10

:

20

:

:

20

:

10.

3 3
3

6
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3

6 Anf. 3 gallons at 55. ; 6 at 5s. 6d.; and 6 at 6s. A grocer would mix teas at 125. 10s, and 6s, with 20 lb. at 45. per lb.; how much of each fort must he take to make the composition worth 8s. per lb. ? Ans. 20 lb. at 45. ; 10 lb. at 6s.; 10 lb. at 1os.; and 20 lb. at 125. How much gold of 159

of

17, and of 22 carats fine, must be mixed with 5 oz. of 18 carats fine, so that the composition may be 20 carats fine ?

Ans. 5 oz. of 15 carats fine, 5 oz of 17, and 25 of 22.

11.

POSITION.

Position is a rule, which, by false or supposed numbers, taken at pleasure, discovers the true one required. It is divided into two parts,

SINGLE and DOUBLE.

SINGLE POSITION

Is, by using one supposed number, and working with it as the true one, you find the real number required by the following.

Rule. As the total of the errors is to the given sum, fo is the fupposed number to the true one required..

PROOF. Add the several parts of the result together, and if it agrees with the given fum, it is right.

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EXAMPLES.

1. A school-master, being asked how many scholars he had, said, If I had as many, half as many, and one quarter as many more, I should have 264; how many had he ?

Suppose he had 72
as many

as many
as many

18
As 198
: 264

72
72

Proof.
528
1848

72 36

96

96 98

24

198)19008(96 Answer.

1782

264

1188 1188

2.

A person, after spending and of his money, had 60 dollars left ; what had he at first ?

Ans. 144

dols. 3. A certain sum of money is to be divided between 4 persons, in luch a manner, that the first shall have 1 of it, the second I, the third , and the fourth the remainder, which is 28 dollars ; what was the sum ?

Anf. 112 dols. 4. A person lent his friend a sum of money unknown, to receive interest for the same, at 6 per cent. per annum, fimple interest, and at the end of 5 years he received for principal and interest 644 dols. 80 cents; what was the sum lent ?

Ans. 496 dollars.

DOUBLE POSITION

Is, by making use of two supposed numbers, which, if both prove false, are, with their errors, to be thus disposed ;

RULE. 5. Place each error against its respective position. 2. Multiply them cross-wife.

3. If the errors are alike, that is, both greater or both less than the given number, divide the difference of the products by the difference of the errors, and the quotient is the answer : Bnt if the errors be un. like, divide the sum of the products by the luin of the errors, and the quotient will be the answer.

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