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number in the same degree larger than 25, that 100
is larger than 80. Ans. 30,3125.
16. If a man lose 26 per cent. by selling 16 bushels of apples for 5 dollars, what did the apples cost him per bushel ? Ans. $0.422.
17. A merchant sells a quantity of paper for 20 dollars, and loses 16 per cent. ; what ought he to sell it for to gain the same per cent.?
18. In what time will 527 dollars gain 158 dol
lars 10 cents, at 6 per cent. interest ?
There will be as many years as the interest of 527 dollars for one year can be taken times from $158,10. Ans. 5 years.
19. G paid H 169 pounds of currents, at 11 cents a pound. for the use of $107,38 a certain time, at 5 per cent. per annum; how long did G keep H’s money 2 Operation. 5, 3 6 9) 1 8, 5 9 0 (3 years. 1 6 1 0 7
Explanation.—The price of the currants is $18,590, and the interest of $107,38 for one year is $5,369. The price of the currants divided by one year's interest, gives the time, which is 3 Y. and #### of another year. Multiplying the numerator of the fraction by 12, the number of months in a year, and dividing by the denominator, gives the value of the fraction in months, which is 544;#. To obtain the value of #### of a month in days, we multiply the numerator by 30, and divide by the denominator, and find 16####, or 16### days. Therefore, the answer is, that G had the use of the money 3 Y. 5 mo. 16### d. (See Explanation to Question 16, page 148; also, Explanation to Question 32, page 197.)
20. A mechanick was to give an apprentice $110 when he should be 21 years old, which took place March 15, 1820. At that time a new contract was made, by which the apprentice was to have the loan of $500 until the interest at 5 per cent. should balance the $110. At what time was the apprentice to repay the $500 ! Ans. August 9, 1824.
21. B gave a note of $400, dated March 31, 1824; and January 1, 1826, when he paid the same, it amounted to $433,25. At what rate per cent. did he pay interest ?
Divide the interest for 1 year by the principal.
The time is 13 years, and 4 of the whole interest is the interest for 1 year ! Ans. 4% per cent.
22. If I pay $42,0875 for the loan of $259 for 3; years, at what rate do I pay interest? Ans. 5 per cent. 23. A has corn worth 73 cents per bushel cash, but in barter he lets B have it for 85 cents, and takes tea which B is selling for 95 cents cash; at what per pound must A receive the tea in barter "
* When one commodity is exchanged for another, the trade is called barter,
The object in this question is to find a number in the same degree larger than 95, that 85 is larger than 83. This will be obtained by taking #3 of 95. Ans. $1,106--
24. If hops, which cost 30 cents per pound, are sold for 34 cents, at what price should pepper be sold, which cost 31 cents per pound, to gain the same per cent. 2 Ans. $0,351 per pound. 25. A shoe-merchant sells 300 pairs of shoes worth $1.35 ready money, for $450, and takes his pay in brick worth $5 per thousand. How many brick does he in equity receive 2 Ans. 81 thousand. 26. In 1810, the number of inhabitants in NewYork was 959,049, and in 1820, 1,372,812. What was the gain per cent. in population from 1810 to 1820 2 Ans. 43,1+. 27. Two men put their money together for the purpose of trading; one put in $500; the other $750. They gained 49 per cent. on their stock; what was the actual gain of each * . Ans. One gained $245: the other $3674: 28. Three men united their capitals in trade; viz. A, $3500; B, $3050; and C, $5000. After continuing in business a certain time, A found his share of the common stock to be worth $4750, What per cent. did they gain; also, what was the value of B and C’s shares? Ans. They gained 353 per cent. B's share $4139,28+, and C’s share $6785,71+. 29. D and E after trading together, found their capital to be worth $3500, and that they had gained 40 per cent. on their original stock. At that time E’s share was $2100; what did they put in respectively 7
Explanation.—Were we to subtract the whole gain from $3500, the remainder would be the stock with which they commenced trade. Now, if we divide what they gained by 40 cents, the quotient will express the number of dollars put into trade, since the gain on each dollar was 40 cents. Also, if we divide
the number of dollars put into trade by one dollar, the quotient will be the same number as the dividend. But if we reduce $3500 to cents, by annexing two ciphers, and divide by 140 cents, every time we take 140 cents from the 350000 cents, we take 1 dollar of the original stock, and 40 cents the gain on that dollar, the quotient will therefore be the same number that we should have obtained had we divided the original stock by 1 dollar, and the gain by 40 cents. This is the shortest method to find the original stock, when the per cent. is given; and the gain and original stock are expressed in the same number. E owned ####, or ; of the stock. Ans. E $1500, and D $1000.
30. A man by trading several years gained $1427, which was 314 per cent. on the money with which he commenced trade. What was his original capital 2 Ans. $4530} }. 31. C after trading awhile with D, took $625, which was # of the whole gain; how much money did D unite with C, allowing they gained 29 per cent.” Ans. $2873.44. 32. W with a capital of $7000, proposes to take X as a partner, whose capital is only $800, on condition that X shall be entitled to of the whole gain by paying Winterest, at 5 per cent., on such part of W’s stock as will make their stocks equal. If their united stocks at the end of one year amount to $8700, what will X gain in the trade? Ans. $295.
Remark.-Most of the questions which occur in business, are solved by the principles already illustrated. . We shall here insert a number of questions, many of which will vary in some respects from those which have been given, but all of them may readily be worked by the student who has obtained a know
ledge of the principles explained in the preceding sections, without particular rules. When a question is given, the first object of the student should be, to study well the value of the question; to ascertain what is required, and by what means that result may be obtained. o One reason why scholars are so often perplexed in working questions in arithmetick, is because they go to work before they distinctly understand the precise object to be obtained.
QUESTIONS TO BE SOLVED BY THE PRINCIPLES
1. What number equals 5 times the sum of 69. and
127 and 1000 2 Ans. 5980. 2. What number equals of the difference between 2767 and 282 Ans. 30 14. 3. What number must be multiplied by 13 to make a product 1 less than 183? Ans. 14. 4. What number must be divided by 21, that the quotient may be 35 ! Ans. 735.
5. A man bought 35 bushels of barley, and sold the whole for $15. He made $2,75 in the trade; what did he give per bushel 2 Ans. 35 cents. 6. A merchant bought 76 gallons of brandy, at 91 cents per gallon, and sold the whole for $85,16. What did he gain on one gallon 2 Ans. 211's cents. 7. A merchant bought 5 pieces of cloth, each measuring 31 yards, for $26,35. What did he sell it for per yard to make $5 on the whole 2 Ans. 20 or cents. 8. A gentleman bought a cask of wine containing 46 gallons for 76 cents per gallon. At what must he sell it per gallon to gain $6,27, if three gallons are lost by the cask’s leaking 2 Ans. $0,958+. 9. If a man walk two miles in half an hour, how far can he walk in 6 days, when the days are 104 hours long ' Ans. 252.