Ex. 2. An engineer having raised 100 yards of a certain work in 24 days with 5 men; how many men must he employ to finish a like quantity of work in 15 days? ds 5 ds men men 15 ) 120 ( 8 Answer. 120 3. What will 72 yards of cloth cost, at the rate of 9 yards for 51 12s ? Ans. 441 16s. 4. A person's annual income being 1461; how much is that per day? Ans. 8s. 5. If 3 paces or common steps of a certain person be equal to 2 yards, how many yards will 160 of his paces make? Ans. 106 yds 2 ft. 6. What length must be cut off a board, that is 9 inches broad, to make a square foot, or as much as 12 inches in length and 12 in breadth contains ? Ans. 16 inches. 7. If 750 men require 22500 rations of bread for a month; how many rations will a garrison of 1200 men require ? Ans. 36000. 8. If 7 cwt 1 ar cost 261 10s 4d; what will be the price of 43 cwt 2 qrs? Ans. 1591 25. 9. The clothing of a regiment of foot of 750 men amounting to 28311 5s; what will the clothing of a body of 3500 men amount to? Ans. 132121 10s. 10. How many yards of matting, that is 3 ft broad, will cover a floor that is 27 feet long and 20 feet broad? Ans. 60 yards. 11. What is the value of 6 bushels of coals, at the rate of 1/ 14s 6d the chaldron ? Ans. 5s 9d. 12. If 6352 stones of 3 feet long complete a certain quantity of walling; how many stones of 2 feet long will raise a like quantity ? Ans. 9528. 13. What must be given for a piece of silver weighing 73 lb 5 oz 15 dwts, at the rate of 5s 9d per ounce ? Ans. 2531 10s ozd. 14. A garrison of 536 men having provision for 12 months; how long will those provisions last, if the garrison be increased to 1124 men ? Ans. 174 days and 44 15. What will be the tax upon 7631 15s, at the rate of 3s 6d per pound sterling? Ans. 133/ 13s 1d. 16. A certain work being raised in 12 days, by working 4 hours each day; how long would it have been in raising by working 6 hours per day? Ans. 8 days. 17. What quantity of corn can I buy for 90 guineas, at the rate of 6s the bushel? Ans. 39 qrs 3 bu. 18. A person, failing in trade, owes in all 977/; at which time he has, in monėy, goods, and recoverable debts, 4201 6s 34d; now supposing these things delivered to his creditors, how much will they get per pound? Ans. 8s 7 d. 19. A plain of a certain extent having supplied a body of 3000 horse with forage for 18 days; then how many days would the same plain have supplied a body of 2000 horse?' Ans. 27 days. 20. Suppose a gentleman's income is 600 guineas a year, and that he spends 25s 6d per day, one day with another; how much will he have saved at the year's end? Ans. 1641 12s 6d. 21. What cost 30 pieces of lead, each weighing I cwt 12lb, at the rate of 16s 4d the cwt? Ans. 271 2s 6d. 22. The governor of a besieged place having provision for 54 days, at the rate of 11 lb of bread; but being desirous to prolong the siege to 80 days, in expectation of succour, in that case what must the ration of bread be? Ans. 1 lb. 23. At half a guinea per week, how long can I be boarded for 20 pounds ? Ans. 38127 wks. 24. How much will 75 chaldrons 7 bushels of coals come to, at the rate of 12 13s 6d per Ans. 1251 195 0 d. 25. If the penny loaf weigh 8 ounces when the bushel of wheat costs 75 3d, what ought the penny loaf to weigh when the wheat is at 8s 4d? Ans. 6 oz 1573. dr. 26. How much a year will 173 acres 2 roods 14 poles of land give, at the rate of 1/7s 8d per Ans. 2401 2s 7 d. 27. To how much amounts 79 pieces of lead, each weighing 1 cwt 3 qrs 7 lb, at 10l 4s per fother of 191 cwt? Ans. 69/ 4s 2d 145 q. 28. How many yards of stuff, of 3 grs wide, will line a cloak that is 14 yards in length and 3 yards wide ? Ans. 8 yds O qrs 2} nl. 29. If 5 yards of cloth cost 14s 2d, what must be given for 9 pieces, containing each 21 yards 1 quarter ? Ans. 277 1s 10 d. 30. If a gentleman's estate be worth 21071 12s a year; what may he spend per day, to save 5Col in the year ? Ans. 4! 8s 16 d. 31. Wanting 31. Wanting just an acre of land cut off from a piece swhich is 134 poles in breadth, what length must the piece be? Ans 11 po 4 yds 2 ft 0in. 32. At 7s 9 d per yard, what is the value of a piece of cloth containing 53 ells English 1 qu. Ans. 251 18s 12d. 33. If the carriage of 5 cwt 14 lb for 96 miles be 1l 12s 6d; how far may I have 3 cwt 1 qr carried for the same money? Ans. 151 m 3 fur 375 pol. 34. Bought a silver tankard, weighing 1 lb 7 oz 14 dwts; what did it cost me at 6s 4d the ounce? Ans. 61 4s 9 d. 35. What is the half year's rent of 547 acres of land, at 15s 6d the acre ? Ans. 2111 19s 3d. 36. A wall that is to be built to the height of 36 feet, was raised 9 feet high by 16 men in 6 days; then how many men must be employed to finish the wall in 4 days, at the same rate of working ? Ans. 72 men. 37. What will be the charge of keeping 20 horses for a year, at the rate of 141d per day for each horse? Ans. 44 11 Os 10d. 38. If 18 ells of stuff that is yard wide, cost 39s 6d; what will 50 ells, of the same goodness, cost, being yard wide? Ans, 71 6s 32d. 39. How many yards of paper that is 30 inches wide, will hang a room that is 20 yards in circuit and 9 feet high? Ans. 72 yards. 40. If a gentleman's estate be worth 384! 16s a year, and the land-tax be assessed at 25 94d per pound, what is his net annual income? Ans. 3311 1s 9 d. 41. The circumference of the earth is about 25000 miles; at what rate per hour is a person at the middle of its surface carried round, one whole rotation being made in 23 hours 56 minutes ? Ans. 1044 816 miles. 42. If a person drink 20 bottles of wine per month, when it costs 8s a gallon ; how many bottles per month may he drink, without increasing the expense, when wine costs 10s the gallon? Ans. 16 bottles. 43. What cost 43 qrs 5 bushels of corn, at 1l 8s 6d the quarter? Ans. 621 3s 3 d. 44. How many yards of canvas that is ell wide will line 50 yards of say that is 3 quarters wide? Ans. 30 yds. 45. If an ounce of gold cost 4 guineas, what is the value of a grain? Ans. 25d. 46. If 3 cwt of tea cost 401 12s; at how much a pound must it be retailed, to gain 107 by the whole? Ans. 374 COMPOUND COMPOUND PROPORTION. COMPOUND PROPORTION shows how to resolve such questions as require two or more statings by Sinple Proportion; and these may be either Direct or Inverse. In these questions, there is always given an odd number of terms, either five, or seven, or nine, &c. These are distin-, guished into terms of supposition, and terms of demand, there being always one term more of the former than of the latter, which is of the same kind with the answer sought. The method is thus : Ser down in the middle place that term of supposition which is of the same kind with the answer sought. Take one of the other terms of supposition, and one of the demanding terms which is of the same kind with it; then place one of them for a first term, and the other for a third, according to the directions given in the Rule of Three.--Do the same with another term of supposition, and its corresponding demanding term ; and so on if there be more terms of each kind; setting the numbers under each other which fall all on the left-hand side of the middle term, and the same for the others on the right-hand side. -Then, to work By several Operations. Take the two upper terms and the middle term, in the same order as they stand, for the first Rule-of-Three question to be worked, whence will be found a fourth term. Then take this fourth number, so found, for the middle term of a second Rule-of-Three question, and the next two under terms in the general stating, in the same order as they stand, finding a fourth term for them. And so on, as far as there are any numbers in the general stating, making always the fourth number, resulting from each simple stating, to be the second term in the next following one. So shall the last resulting number be the answer to the question. By one Operation.--Multiply together all the terms standing under each other, on the left-hand side of the middle term; and, in like manner, multiply together all those on the right-hand side of it. Then multiply the middle term by the latter product, and divide the result by the former product ; so shall the quotient be the answer sought. VOL. I. EXAMPLES EXAMPLES. 1. How many men can complete a trench of 135 yards long in 8 days, when 16 men can dig 54 yards in 6 days? 432) 12960 ( 30 Ans. by one operatios, 1296 The same by two Operations. 2d. 6 16 2. If 100l in one year gain 51 interest, what will be the interest of 7507 for 7 years? Ans. 2621 105. 3. If a family of 8 persons expend 2002 in 9 months ; how much will serve a family of 18 people 12 months ? Ans. 300% 4. If 27s be the wages of 4 men for 7 days; what will be the wages of 14 men for 10 days ? Ans. 61 15s. 5. If a footman travel 130 miles in 3 days, when the days are 12 hours long; in how many days, of 10 hours each, may he travel 360 miles? Ans. 9 days. Ex. 6.. |