Miscellaneous Questions on all the foregoing Ex. 1. What three numbers are those, the first of which is 105' the second 3ds of the first, and the third 67 less than the first and second together ?* Ex. 2. A gentleman left his eldest daughter 1000 guineas more than the youngest, and to three other daughters he left 7000 guineas between them, which was equal to the sum left to the youngest and eldest together what was each child's fortune? Ex. 3. What is the difference in value between five times five and twenty guineas, and five times twenty-five guineas? Ex. 4. What was the value of a prize taken by 25 sailors, besides officers, so that each sailor received 197. 9s. 9d., and the officers received as much as the sailors? Ex. 5. A prize valued at 13,1777. 10s., after the officers have had their share, is to be divided among 525 sailors: what would each man have to take? Ex. 6. What is a fourth proportional to the numbers 6, 9, and 24?+ Ex. 7. What is the value of 4 packs of cloth, each pack containing 4 parcels, each parcel 10 pieces, and each piece 26 yards, at the rate of 21. 8s. for 3 yards? Ex. 8. How many yards of paper, 3 quarters wide, will be sufficientfor a room 48 yards round, and four yards high: and what is the value of the paper, at the rate of 18s. per piece of 24 yards? Ez. 9. If 100l. months? gain 57. in 12 months, what will 751. gain in nine Ex. 10. If 48 cannon consume, in 3 days, 288 barrels of powder, how much will be spent in 15 days, when 144 cannon are to be supplied? Ex. 11. Fifteen people joined to purchase a lottery ticket, for which they gave three shillings less than eighteen guineas: if it came up a prize of 30,000 guineas, what did each man receive, and what was his gain? -Ex. 12. A tobacconist bought two parcels of tobacco, which weighed 9 cwt. 2 qrs., for a hundred guineas, the difference of the NOTES. To find ds of any number, multiply the number by two, and divide by three: thus, 3ds of a guinea is 21 X 2 3 14 shillings. + A fourth proportional is found, as is evident, rule, p. 92, by multiplying the second and third numbers together, and dividing by the first,; thus a fourth proportional to the numbers 8, 12, and 16, is parcels in weight was 3 qrs. 12lb., and in value eight guineas: what was their weight and values? Ex. 13. The clothing of 100 charity children came to 2117., of which 13 5. was expended on 60 boys: what was paid for the 40 girls, and how much did the cloaths of each child cost? Ex. 14. A great grazier left to his four sons 220 oxen and 1200 sheep I demand the value of each son's legacy, supposing the oxen worth 18 guineas each, and the sheep 39 shillings each ? : Ex. 15. What number is that which, multiplied by 394, will give a product of 3,013,248 ? Ex. 16. What is gained by the sale of 436 yards of broad cloth, that was bought at the rate of 5 yards for 4l. 15., and sold at the rate of 61. 4s. for 6 yards? Ex. 17. If 9 printers can set up the New Testament in 22 days, in what time could it be done if 15 were employed? Ex. 15. If s pressmen will, on the average, earn 147. 8s. in six days, how much can 15 men earn in 27 days? Ex. 19. When the quotient is 1083, and the divisor 555, what is the dividend, if there be remainder of 79 ? Ex. 20. There are about 800 new books and pamphlets published, every year in London, the value for one copy of each work is estimated at 240l. what is the average value of each book? Ex. 21. If each of the 800 publications contain on an average 15 sheets, and of each there be 1250 copies printed, I demand how much paper is used in the business, and its value, allowing to each ream of paper 500 sheets, and the price of it at 25s. 6d. per ream ?* Ex. 22. The silk mill at Derby winds off 73,726 yards of silk every time the great wheel goes round, which is thrice in a minute: how many yards will it wind in a year, allowing that it works every day, except Sundays, 15 hours, and how many skeins will be made, sup. posing 960 yards ge to the skein? Ex. 23. In the partition of some waste lands in the west of England, A had 591 acres, B 76 acres, C 110 act. gr. 12 per., D 1.5 acres, and E 39 acı. Or. 12 per., but these, taken together, were but one-fifth of the whole: how many acres were divided, and what was the value of the whole, supposing each acre worth 51. 9s. 6d. ? Ex. 24. An island in the West Indies contains 42 parishes, and every parish 76 houses, and each house at the rate of 5 white persons; besides these, there were 65 negroes to each of 54 plantations: how many people were there on the whole island? Ex 25. In the club mentioned in the Spectator (No. 9), there were 15 persons, weighing together 3 tons; how many pounds, ounces, and drams, Avoirdupois, did each man weigh? Ex. 26. The British possessions in Hindostan contain 212,406 square miles, and the population is estimated at fourteen millions: how many nhabitants are there to a square mile? NOTE. *This, and the preceding question, do not include the new editions f books. Ex. 27. If 9 lb. of tea cost 31. 7s. 7d., what is the worth of four chests, each weighing one hundred and a half? Ex. 28. What shall I give for a farm containing 256 acres and a half, for which I am to pay at the rate of 95 guineas for three acres? Ex. 29. What will it cost a young man to come into a farm, for the lease of which he is to pay 1000 guineas; for 22 horses he is to pay at the rate of 18 guineas each; for crops in the ground 3547.; for 210 bushels of wheat he is to pay 4l. 10s. per quarter; the household furniture is appraised to him at 298 guineas, and for farming utensils of all kinds he is to pay 1961.? Ex. 30. The revenue collected in Hindostan, by the British, is reckoned at 3,400,000l., how much is that from each inhabitant, supposing they amount to 14 millions? Ex. 81. The number of nergoes in Jamaica is estimated at 250,000, and of whites at 20,000, how many slaves are there to a single white man, and what do the planters reckon their property worth in the article of slaves only, supposing each to be worth 93 guineas? Ex. 32. The population in the United States is estimated at six millions and a half, and the number of slaves still existing in that free country is reckoned to be 697,697, how many free people are there to one slave? Ex. 33. The extent of China Proper is equal to 1,397,999 square miles, and the population is estimated at 333,000,000, how many inhabitants are there to a square mile? Ex. 34. In Spain each person pays 10 shillings to government for protection; in France, under the old government, each paid 20s, for protection; and in England we pay full three guineas each for the same advantages, how much is the revenue of the three governments, supposing the population of Spaino be 10 millions; of France, at the period referred to, 25 millions; and of England and Wales 9,343,173? Ex. 35. The population of London, Westminster, and Southwark, is 864,865, that of Paris 547,756, how much does the population of London exceed that of Paris? Ex. 36. How many minutes and seconds have elapsed since the birth of Christ, or 1-808 years? Ex. 37. How long would it require to count five hundred millions sterling, supposing a person were to reckon 150l. in a minute, and were to be employed 10 hours each day, and six days a week, till he had finished the job? Ex. 38. How many barley corns will reach round the earth, supposing the length to be 25,200 miles? Ex. 39. How many seven-shilling pieces are there in a thousand pounds? Ex. 40. A French franc is worth 10d., how many francs are there in 100l.? Ex. 41. If 8 men can mow 18 acres in 4 days, how many men will be required to mow 50 acres in six days.? Ex. 42. A balloon has moved at the rate of 6492 feet in a minute, how long would it have been sailing round the earth at the same rate, supposing the circumference of the earth to be 25,200 miles? Ex. 43. How much oftener will the small wheel of a coach turn than the large one, between London and Bristol, or 120 miles, if the former be 10 feet 8 inches in circumference, and the latter 18 feet 4 inches? Ex. 44. If my income be 250l. per annum, and I have foolishly expended 15s. per day, how much shall I be in debt at the year's end, and what may I expend per day the following year, so as to have ten guineas in hand at the conclusion of it? Ex. 45. It is said the impositions of hackney-coachmen, by overcharges, are equal to one-fourth of what they earn: now, if they earn each on an average 18s. per day, and there be 1100 employed 313 days in a year, I demand the amount of their overcharges in a year? Ex. 46. There were at Vauxhall gardens on the Prince of Wales's birth-day, 1805, 10,059 persons: the admission money was 3s. each; now, supposing each person to spend 3s. more, the half of which was profit to the proprietor, what would he clear by the night, allowing that the incidental expenses were 250l.? Ex. 47. How much time, in the course of 30 years, docs a person gain, who rises at five o'clock in the morning, over another who lies till eight, supposing both go to bed at half past ten at night, and supposing the year to consist of 365 days? Ex. 48. If 8 yards of cloth will make a shirt, how much of the same stuff will be wanted to make two shirts for each man of a regiment, consisting of 855 men? Ex. 49. In November, 1800, 276,334 five-pound bank notes were issued; in December 2,626,700; and in the January following 2,769,160: what was the nominal value of the notes issued in these three months; and what was the cost of white rags, from which they were made, supposing each ounce of rag might be manufactured into twenty five-pound notes, and the rags to be worth 8d. per lb. ? Ex. 50. Two persons depart from London for York on the same day; the one walks 19 miles a day, the other only 15 miles: how far distant will they be from one another after ten days travelling, and when will each get to York, which is 197 miles from London? Ex. 51. The population of the world is estimated at a thousand millions of human beings: if the face of the earth be re-peopled every 33 years, how many persons are born and die in a year, week, day, and minute ?* Ex. 52. The field opposite my house will serve 50 cows forty days: how long will it afford 220 with equal feed? Ex. 53. If 10 persons expend 250l. in 4 months: how much ought 3 persons to expend in 12 months? NOTE. * The number of persons that are born and die in a year is 1,000,000,000 divided by 33. FRACTIONS. A Fraction is the part, or parts of a whole, or of any whole quantity expressed by unity, and is expressed by two figures, with a line drawn between them, as 1, †, f. The upper figure of a fraction is called the numerator, and the under one the denominator. The denominator shews how many parts the unit is divided into, and the numerator how many of these parts are to be taken; thus, or three-fourths, shews that the whole is divided into four parts, and that three of those parts are to be taken; and g, or five-eighths, shew that the whole is divided into eight paits, and that five of these parts are taken. There are four sorts of fractions, simple und compound, proper and improper. A simple fraction has only one numerator and denominator, as }, or 3. A compound fraction consists of two or more parts, and is known by the word of placed between them, as 3 of 6; or 3 of 3 of 15. A proper fraction is, when the numerator is less than the denominator. An improper fraction is, when the numerator is equal to, or greater than, the denominator. A mixed number is formed from an integer and a fruction joined together, as 8. A complex fraction is one that hus a fraction or a mixed number for its numerator, or denominator, or both. |