3. A man would mix 10 bushels of wheat at 4s. per bushel, with rye at 3s., barley at 2s., and oats at 1s. per bushel; how much rye, barley, and oats must be mixed with the 10 bushels of wheat, that the whole compound may be sold at 28d. per bushel? 4. A man being determined to mix 12 bushels of oats at 1s. 6d. per bushel, with barley at 2s. 6d., rye at 3s., and wheat at 4s. per bushel; I demand how much rye, barley, and wheat must be mixed with the 12 bushels of oats, that the whole compound may be afforded at 2s. 9d. per bushel? Ans. 1. 60 bushels of barley, 60 of rye, and 12 of wheat. Ans. 2. 2 bushels 13 peck of barley, 2b. 1 3p. of rye,and 12 of wheat. Ans. 6. 14 bush. 13 peck of barley, 2b. 13p. of rye, 14b. 13p.of wheat. CASE 3. When the prices of all the ingredients, the quantity to be compounded, and the mean rate of the whole composition are given, to find how much of each ingredient will be necessary to make up the quantity required. RULE. Find the differences between the price of each ingredient, and the mean rate of the whole composition, and place them alternately, as in case the 1st; then say As the sum of all the differences, Is to the quantity to be compounded; To the quantity required at that rate. 1. Suppose I have four sorts of currants, viz; at 8 cents, 12 cents, 18 cents, and 22 cents per pound; the worst will not sell, and the best are too dear, I therefore conclude to make a composition of 120 pounds, which I propose selling at 16 cents per pound. How much of each sort will be required? 2. How many gallons of water must be mixed with wine at 48cts. per gallon, so as to fill a vessel of 80 gallons, that may be sold at 33cts. per gallon? Ans. 25 of water. 3. How much sugar at 10cts., 12cts., and 15cts. per lb., will be required to compose a mixture of 240lbs. that may be sold at 13cts. per lb. ? Ans. 60lbs. at 10cts; 60lbs. at 12cts., and 120lbs. at 15cts. per lb. ? 4. How much gold of 15; of 17, of 20, and of 22 carats fine, must be melted together, to form a composition of 40oz. of 18 carats fine? Ans. 1. 16oz. of 15 carats, 8oz. of 17 carats, 4oz. of 20 carats, and 12oz. of 22 carats fine.-Ans. 2. 8oz of 15 carats, 16oz. of 17 carats, 12oz. of 20 carats, and 4oz. of 22 carats fine.-Ans. 3. 12oz. of 15 carats, 12oz. of 17 carats, 8oz. of 20 carats, and 8oz. of 22 carats-fine. The student will please to find the four remaining answers, and prove them all by Alligation Medial. POSITION. Position is a rule which teaches us how to find an unknown number, by using one or more supposed numbers. It is divided into two parts, namely, Single and Double. I. OF SINGLE POSITION. Single Position teaches us how to resolve those questions whose answers are proportional to their suppositions: that is, such as require the multiplication or division of the number sought by any proposed number; or, when it is to be increased or diminished by itself, or any part or parts of itself, a given number of times, &c. RULE. Choose any convenient number at pleasure, and work with it a greeably to the tenor of the question; then say, As the result of the operation, Is to the supposed number; To the number required. PROOF. Work with the answer according to the tenor of the question, and the result will be equal to the given number. N. B.-Many questions which are commonly wrought by Position, may be solved very concisely by Vulgar Fractions without a supposition. EXAMPLES. 1. What number is that of which the 1, 3, and will make 104 ? Suppose the number to be 60, Then of 6030 Examine the same question worked by Vulgar Fractions. 26 13 numerator. or, 24 12 denom. N. D. given As 13 12 :: 104 number. 12 13)1248 Ans. 96 as before. 2. A person after expending and of his money, had $60 left; how many had he at first? Now + expended, and 13, or 1—3= left; therefore As 5: 12: 60.. $144 Ans. 3. A, B, and C bought a quantity of goods amounting to $612, of which sum A paid three times more than B and B four times more than C; how much did each man pay? A paid $432, B $144, and C $36. 4. A man overtaking a maid driving a flock of geese, said to her, how do you do, sweetheart? where are you going with your 40 geese? Indeed, sir, said she, I have not 40, but if I had as many more, half as many more, and 10 geese besides, I should have 40. How many geese had she? Ans. 12 geese. 5. Suppose I have a cistern full of water, with three unequal pipes: now the greatest pipe will empty the cistern in one hour, the second in two, and the third in three. In what time will the cistern be emptied, if all three of the pipes are left open at once? Ans. 32 minutes 43 seconds. 6. What is the age of a person who says, that, if of the years I have lived be multiplied by 7, and 3 of them be added to the product, the sum will be 292? Ans. 60 years. 7. A schoolmaster being asked how many scholars he had, answered, if to double the number I now have you add §, 1, 1, and of them, I shall have 435; how many scholars had he? Ans. 120. 8. What sum will amount to $860 in 12 years, at $6 per cent. per annum? Ans. $500. 9. A certain sum of money is to be divided among A, B, C, D, and E, in such a manner that A may have 1, B, C, D, and E the remainder, which is $40; what is the sum and each man's share of it? Ans. The sum is $100, of which A gets $25, B 20,, € 10, D 5, and E the rest, which is $40. age 10. A man after expending and of his yearly income, had $263 left; what did his yearly salary amount to? Ans. $160. 11. When A, B, and C were talking of their ages, B said his was equal to 1 times the age of A, to which C replied, I am twice and the age of you both, and the sum of our ages is equal to 93; what was the age of each person? Ans. A was 12, B 18, and C 63 years of age.. 12. A man having found a bag of dollars, said that the 3, 4, 1, and of them made up the sum of 57; please to tell me how many dollars were in the bag? Ans. $60. 13. The yearly interest of Miss Charlotte's money, at $6 per cent., exceeds one-twentieth of the principal by $100, and she does not intend to marry any man who is not scholar enough to tell the amount of her fortune. Pray, sir, can you obtain her consent? Yes, sir, she is worth exactly $10000. II. OF DOUBLE POSITION. Double Position teaches us how to resolve questions by making use of two supposed numbers. Those questions in which the results are not proportional to their suppositions, belong to this rule : that is, such as those in which the number sought is increased or diminished by some given number which is not any known part of the number required. RULE. 1. Suppose any two convenient numbers, and work with each of them agreeably to the tenor of the question, and if the error be too great in either of the operations mark it with +, but if it be too small mark it with-. 2. Multiply the first position by the second error, and the second position by the first error. 3. If the errors be alike, that is, both greater or both less than the given number, take their difference for a divisor and the difference of the products for a dividend. 4. If the errors be unlike, that is, one too much and the other too little, then take their sum for a divisor and the sum of the products for a dividend; the quotient in either case will be the number required. PROOF. Work with the answer according to the conditions of the ques-. tion, and the result will be equal to the given number. EXAMPLES. 1. A man was hired 50 days on these conditions, that is, for every day he worked he should receive 75 cents, and for every day he was idle he should forfeit 25 cents; at the expiration of the time, |