Brought over 1350 1092 258 4 1092)1032(0qr. Note 1. If you look at the stating, you will see that the first and third terms are of the same kind, but of different denominations, and therefore are reduced to the same name or denomination, and that the demand of the question lies on the 3d term. 2. That the middle term, being given in pounds, shillings and pence, is reduced to pence. But, 3. If the second term were in federal money, it would be sufficient to proceed according to decimals. Thus: if the price were $92 91c. 7m, D. c. m. 拈 # As 1092 92·917 :: 263: the Ans. 263 278751 557502 185834 D. c. m. 1092)24437-171(22.378+, Ans. 2184 2597 2184 4131 3276 8557 7644 9131 8736 395 12. If 57yds. cost £69 what will 9yds. cost at that rate? yds. £ yds. As 57: 69:9 9 57)621(£10 17s. 10d. 234qrs. Ans. Here, all the terms being whole numbers, there is no need of reducing the middle one until after stating. The same in Federal money would stand thus: 13. If my income be 109 guineas per annum, I desire to know what I may spend per day, so that I may lay up £45 at the year's end? Ans. £0 5 1035 per day. Note 1. You must subtract £45 from the value of 109 guineas. 2. There being 365 days in a year, your question must next be stated thus: s. d. qr. D. Guin. £ D. 365 As 365 109-45 :: 1 : 5 10 31 the Ans. 14. If my salary be £43 12s. 5d. per annum, what does it amount to per week? The Stating. W. £ s. d. W. As 52 43 12 5: 1: the Ans. D. Ans. £0 16s. 91d. Note. As there are 52 weeks and 1 day in a year, you will get the true answer to the above question by the following ratio. £ s. d. D. 15. Suppose my income to be 16s. per annum? 51 365 43 12 5 7: 16s. 8333d. 8383d. per week, what is it Ans. £43 13s. 7 d. Note 1. You must first reduce the middle term to pence. 2. You must multiply by 365 (the denominator of the fraction) and add to the product the 283 which remains; and remember always to do so in similar cases. 3. You must divide by 7, the first term and the quotient will be the answer in 365ths of a penny, which (in all similar cases) must be first divided by the denominator, and then brought into pounds. 16. If I am to pay 1s. 7d. per week for pasturing a cow; what must I give per week for 37 cows? £2 18s. 7d. Ans. 17. How. many yards of cloth may be bought for $195 75c. of which 91yds. cost $11 2c.? 168yds. 3qrs. Ans. 228 18. If I buy 57 yards of cloth for 49 guineas; what did it cost per ell English? £1 10s. 13d. Ans. 19. A merchant, failing in trade, owes in all £3475, and has in money and effects but £2316 13 4: Now, supposing his effects are delivered up, pray, what will each creditor receive on the pound? £ s. d. £ £ As 3475: 2316 13 4 :: 1: £0 13s. 4d. Ans. 20. A owes B £3475, but B compounds with him for 13s. 4d. on the pound; pray, what must he receive for his debt? £2316 13s. 4d. Ans. 21. If the distance from Newburyport to York be 31 miles; I demand how many times a wheel, whose circumference is 15 feet will turn round in performing the journey? 10560 times, Answer. 22. Bought 9 chests of tea, each weighing Scwt. 2qrs. 211b. at 24 9s. per cwt. what came they to? £147 13s. 81d. Ans. 23. What will 371 gross of buttons come to at 13 cents per Rozen? $58 50c. Ans. 24. A farm, containing 125 A. 3r 27p. is rented at $11 50c. per acre; what is the yearly rent of that farm? $1447 6c. 5m. Ans. 25. If a ship cost £537 what are of her worth? Eigh. £ Eigh. £ s. d. As 8: 537 :: 3 : 201 7 6 Ans. 26. If of a ship cost $1163 what is the whole worth? $2658 28c. 5m. Ans. 27. Bought a cask of wine at 76c. 5m. per gallon, for $125; How much did it contain? 163gal. 1qt. 1 pt. Ans. 28. What comes the insurance of £537 15s. to, at £41 per centum? £ s. £ s. d. £ £ As 100 4: 537 15: 24 3 1111% 8 Ans. 29. What come the commissions of £785 to at 3 guineas per cent? £38 9s. 31 d. Ans. 30. A merchant bought 9 packages of cloth, at 3 guineas for 7 yards each package contained 8 parcels, each parcel 12 pieces, and each piece 20 yards; how many dollars came the whole to, and how many per yard? Yds. gain. pack. $ As 7: 39: 34560 Ans. for the whole cost. As 7 3 1: 2 Ans. per yard. 31. A merchant bought 49 tuns of wine for $910; freight cost $90; duties $40; cellar $31 67c.; other charges $50 and he would gain $185 by the bargain; what must I give him for 23 tuns? Tuns. $ $ $ $ c. $ $ Tuns. $ As 49 910+90+40+31 67+50+185 :: 23: 613 33c Ans. 32. If $100 gain $6 in a year, what will $475 gain in that time? Ans. $28 50c. 33. The earth being 360 degrees in circumference, turns round on its axis in 24 hours; how far does it turn in one minute, in the 43d parallel of latitude; the degree of longitude, in this latitude, being about 51 statute miles? H. D. M. M. M. As 24: 360 × 51: 1: 123 Ans. 34. Shipt for the West Indies 225 quintals of fish, at 15s. 6d. per quintal; 37000 feet of boards, at 81 dolls. per 1000; 12000 shingles, atguin. per 1000; 19000 hoops at $1 per 1000, and 53 half joes; and in return, I have had 3000 galls. of rum, at 1s. 3d. per gallon; 2700 gallons of molasses, at 5d. per gallon; 1500 of coffee, at 8d. perib; and 19cwt. of sugar, at 12s. 3d. per cwt. and my charges on the voyage were £37 12s. pray, did I gain or lose, and how much by the voyage? Ans. lost £134 9s. 9d. 35. If a staff, 4 feet long, cast a shade (on level ground) 7 feet; what is the height of that steeple, whose shade, at the same time, measures 198 feet ?* F.sh. F.hei. F.sh. F.hei. As 7 4 198 : 1134 Ans." *As the rays of light from the sun may be considered parallel, the lengths of the shadows must be proportioned to the heights of the objects. Hence the reason of the statement of this question. *36. Suppose a tax of $755 be laid on a town, and the inventory of all the estates in the town amounts to $9345, what must A pay whose estate is $149? It may not be amiss to show the general method of assessing town or parish taxes. First, then, an inventory of the value of all the estates, both real and personal, and the number of polls for which each person is rateable, must be taken in separate columns: The most concise way is then to make the total value of the inventory the first term, the tax to be assessed the second, and $1 the third, and the quotient will show the value on the dollar : 2dly, make a table, by multipliplying the value on the dollar by 1, 2, 3, 4, &c.-3dly, From the inventory take the real and personal estates of each man, and find them separately in the table, which will shew you each man's proportional share of the tax for real and personal estates. Note. If any part of the tax is averaged on the polls, or otherwise, before stating to find the value on the dollar, you must deduct the sum of the average tax from the whole sum to be assessed: for which average you must have a separate column, as well as for the real and personal estates. EXAMPLE. Suppose the General Court should grant a tax of $500000, of which the town of Newburyport is to pay $5312 50c. and, of which the polls, being 1550, are to pay $1 25c. each :-The town's inventory amounts to $450000, what will it be on the dollar, and what is A's tax, whose estate (as by the inventory) is as follows, viz. real $1376, personal $1149, and he has polls? Pol. $c. Pol. $ C. First, As 1 1 25 1550: 1937 50 the average part of the tax to be deducted from $5312 50c. and there will remain $3375. $ $ $ Secondly, As 450000 : 3375 :: 1: 74m. on the dollar, 37. If 50 gallons of water, in one hour, fall into a cistern, containing 230 gallons, and by a pipe in the cistern 35 gallons run out in an hour; in what time will it be filled? Ans. 15h. 38. A butcher went with £416, to buy cattle: Oxen, at £22 each, cows at £4, steers at £3 10s. and calves at £2 10s. and of each a like number; how many of each could he purchase with that sum? Ans. 13 each. 39. Said Harry to Dick, my purse and money are worth 34 guineas, but the money is worth eleven times as much as the purse; pray, how much money is there in it? Ans. £4 3s. 5d. 40.* If of a yard cost of a £, what will of a yard cost? 4×7÷1=223£ Answer. ×3×7=}}}£= £1 79. 133d. Or: As 41. There is a cistern, having four cocks; the first will empty it in ten minutes; the second in 20 minutes; the third in 40, and the fourth in 80 minutes; in what time will all four, running together empty it? 42. A and B depart from the same place, and travel the same road; but A goes 5 days before B, at the rate of 20 miles per day; B follows at the rate of 25 miles per day: In what time and distance will he overtake A? M. M. D. M. D. D. D. M. D. M. As 25-20: 1 :: 20×5: 20. And, As 1: 25 :: 20: 500 43. If the earth revolves 366 times in 365 days, in what time does it perform one revolution? Ans. 23h. 56′ 3′′ 56"+=1 Sidereal day.† 44. If the earth makes one complete revolution in 23h. 56′3′′+, in what time does it pass through one degree? Ans. 3' 55" 20" 45. If the earth performs its diurnal revolution in a solar day,‡ or 24 hours; in what time does it move one degree? Ans. 4' 46. Sold a cargo of flax seed in Ireland, for £1795 10s. Irish money; what does that amount to, in Massachusetts currency, £81 5s. Irish being equal to £100 Massachusetts. Ans. £2209 16s. 11d. * If the first term of the statement be a Vulgar Fraction, whether the other terms are or not, after the first and third terms are reduced to the same denomination, invert the first term as in division of Vulgar Fractions, and the product of the three terms will of course be the answer. The student should work the questions in Vulgar, or Decimal Fractions, according as the rules for fractions require. † A sidereal day is the space of time which happens between the departure of a star from, and its return to the same meridian again. The solar day is that space of time which intervenes between the sun's departing from any one meridian, and its return to the same again. S |