11. A, of Valentia, is indebted to B, of Philadelphia, 875 pisastres, 6 rials, 25 marvadies plate: what number of dollars is A charged in B's books? Ans. $700.67 Philadelphia. 12. Exchange for $6403.76. Thirty days after sight, pay this my second of exchange, first of like tenor and date not paid, to Samuel Smith, or order, six thousand four hundred and three dollars, seventysix cents, value received; which charge to John Jones. Don Juan Angelo, merchant, Barcelona. Required the amount of the above bill of exchange in Spanish piastres. Ans. 8004.7 13. In 14958 piastres, 6 rials plate, how many dollars? Ans. $11967. 14. P, of Philadelphia, receives of A, of Amsterdam, an invoice of goods, amounting to 10235 florins, 17 stivers, 8 pennings: how much Pennsylvania currency must be remitted to discharge the bill, at 354 d. per florin? and what is the sum in sterling, exchange at 38 s. 6 d. Flemish per £ sterling? Ans. S£1503 7 s. 10 d. currency. £886 4 s. 51⁄2 d. sterling. 15. A bill for 2524 pesos, 7 rials, 33 marvadies, being remitted to Cadiz; what sum, Pennsylvania currency, is equivalent to it, at 7 s. 6 d. per peso? Ans. £946 17 s. 5 d. 16. A Virginia merchant shipped tobacco to Norway, worth £1743 16 s. Virginia currency; how many rix dollars, at 6 s. each, must he receive? Ans. 5812 dols. 4 s. 17. P, in Philadelphia, owes A, of Amsterdam, $1190; how many guilders is it, at 40 cts. per guilder? Ans. 2975 guilders. 18. What must be paid in Philadelphia, for an invoice of goods charged at 591 florins, 17 stivers, allowing the exchange at 40 cents per florin, and freight and duties 50 per cent. ? Ans. $355.11. 19. In 12843 marks, how many dollars, allowing 33 cents per mark? Ans. $4281. 20. A merchant imported from England 700 ells of cloth, at 5 shillings sterling per ell, the cost of transportation, and duty of the whole amount was 35 per cent., the exchange at par; how many cents must 1 yard be sold for in Philadelphia, to gain 12 per cent.? How many cents 1 yard. yd. 14 qrs. qr. 1 E. E. E. E. 15 shill. shill. 28. $1100 cts. cts. 100 135 cts. duty, &c. 135 cts. Ans. 21. What will 7500 arsheens of ravens-duck cost, at 14 rubles for 50 arsheens? required the cost in rubles, and also in federal money. Ans. 2175 rubles=$1631.25. To change bank into current money. RULE. Say-How much current equal the bank given, when 100 bank is equal to 100+agio current? EXAMPLE. 22. What is the amount in current money of 3000 guilders bank money, the agio being 3 per cent. ? How much current 3000 guilders B. B 100 103 d. 3105 current. Ans. To change current into bank money. RULE. Say-How much bank equals the current money given, when 100+agio current, equal 100 bank? EXAMPLES. 23. What will 3105 guilders current money, amount to in bank money, the agio being 3 per cent.? Ans. 3000. 24. Change 794 guilders, 15 stivers current money, into bank florins, agio 43 per cent. Ans. 761 guilders, 8 stivers, 11 pennings. 25. Reduce 761 guilders, 9 stivers bank money, into current money, agio 43 per cent. Ans. 794 guilders, 15 stivers, 4 pennings.. 26. In £290 11 s. 10 d. sterling, how many pounds Flemish; exchange at 33 s. 10 d. Flemish per £ sterling, and agio at 4 per cent.? Ans. £513 14 s. 1 d. 27. How many dollars will pay for an invoice of tea, amounting to 6446 tales, 1 mace, 6 candareens ? Ans. $9540.31+ 28. In $1656, how many pagodas of India? Ans. 900. 29. Reduce 600 pagodas of India to dollars. 30. In $412, how many rupees of Bengal? Ans. $1104. Ans. 825 rupees. 31. A merchant in Philadelphia receives from Liverpool, goods charged in the invoice at £450 10 s. sterling, which he immediately sells at an advance of 78 per cent.: what is the amount in Pennsylvania currency, also in federal money? Ans. { £801 17 s. 91 d. $2138.37. 32. A, of Paris, draws on B, of London, for 1200 crowns, at 55 d. sterling per crown; for the value whereof, B draws again on A, at 56 d. sterling per crown; besides commission of per cent., what did A gain or lose by this transaction? Ans. Gained 151⁄2+ crowns. NOTE. The method of equations, or chain rule, as it has sometimes been called in this work, for solving the various questions in Arithmetic, may be very clearly demonstrated in this place. Let A, B, C, D, &c. be several denominations of money, and m, n, p, q, r, &c. the numbers or quantities of those denominations, and let them stand thus: Now to find what number of the last denomination (E), is equal to a given number of the first denomination (A), let x times the last term = y times the first, that is, let x E = y A. Multiply all these equations together, the antecedents by the antecedents, and the consequents by the consequents, and we shall have m A × p B × r C × t D × x E = n B× qCxs DX v Exy A. When reducing this equation, we have mprt x = nqs vy. Consequently, if the number of the last denomination be A POWER is the product arising from the multiplication of a given number into itself continually a certain number of times; thus, 2 x 2 = 4 the second power, or square of 2. 8 the third power, or cube of 2. 2 × 2 × 2 × 2 = 16 the fourth power of 2, &c. 2 × 2 × 2 = The number denoting the power is called the index, or exponent of that power; and it is always 1 more than the number of multiplications used in producing the same. Powers that are to be raised, are usually denoted by placing the index above the root; thus, 22 23 24 = = = 4 the 2d power of 2. 8 the 3d power of 2. 16 the 4th power of 2. And 3205 denotes the 5th power of 320, &c. When two or more powers are multiplied together, their product is that power whose index is the sum of the indices, or exponents of the factors or powers multiplied. Thus in the following powers of 2: Indices 1 2 3 Powers 21 22 23 = 4 5 6 7 8 9 10 16 16 and 2 + 2 = 4 index. 7 index. 1024 and 4 + 6 = 10 index. 16384 65536 262144 8th power. 416 64 256 1024 4096 981 729 6561 59049 531441 4782969 43046721 387420489 EXAMPLES. 1. What is the square of 11? 2. What is the square of 22? Ans. 121. Ans. 484. 3. What is the third power or cube of 35? Ans. 42875. OR, EXTRACTING OF ROOTS. EVOLUTION is the reverse of involution, and is the extracting of the roots from the powers given. The root of any number or power, is such a number as, being multiplied into itself a certain number of times, will produce that powThus, 2 is the square root of 4, because 2 x 2 =4; and 4 is the cube root of 64, because 4 x 4 x 4 = 64, &c. er. 9th power. |