2. Having reduced the fractions, and stated the question, as before directed; 3. Multiply the donominator of your first number into the numerators of the second and third, for a new numerator; then multiply the namerator of the first number into the denomi. nator of the second and third, for a new denominator, and place it under the new numerator, for an answer, which reduce to its proper quantity: or invert the first term, and then proceed as in Case 2, Sect 38; or as in Multiplication. EXAMPLES. (1) If 2 yards of silk cost 31. what will.45 yards cost at the same rate ? (2) Ife of a lb. cost 5s. 6d. what will 42} lb. of the same cost? (3) Suppose I give 14s. 8d. for cwt. what must be given for & cwt. of the same at that rate ? (4) A merchant makes an assurance upon a ship and cargo bound to a certain port, value 27001. 10s. and agrees to pay 10 guineas per cent. To what comes the pre mium or charges of the assurance? (5) How much South-sea stock, at 112l. per cent. will 12701. purchase? (6) A mercer bought 4 pieces of silk, each piece containing 223 yards, and was to give Us. 9d. per yard. I demand the value of the whole. (7) If I give 100l. 108. 6d. for 12 pieces of Holland, at the rate of 5s. 6 d. per ell Flemish; I demand how many elis English each piece contained. XLIV. THE RULE of THREE INVERSE, In VULGAR FRACTIONS. AS I observed in the Rule of Three Direct, of there being two methods of performing it, so likewise in this. RULE. 1. Prepare the fractions as before directed, and then proceed as in Sect. 13,- Or, 2. Multiply the denominator of the third number into the numerator of the first and second for a new numerator; then multiply the numerator of the third number into the denominator of the first and second, for a denominator, which place under the numerator for an answer, and find the proper quantity as before; or invert the last term, and proceed as in the last rule. а EXAMPLES. (1) A. lends B. 25}l. for 6 months. How long ought B, to let A. have 101. to requite his kindness ? (2) If 4 men can do a piece of work in 12 hours, in how many hours will 12 men do the same? (3) If the penny loaf weigh 12} oz. when the bushel of wheat is sold for 5s. what is the load worth when the penny loaf weighs 8 oz.? (4) Suppose A. lends to B. 100ğl, for 6 months, what sum must B. lend A. for 3 years to requite him? (5) How many yards of cloth, at 8s. 6d. per yard, must be given for 20 í yards, at 5s. 7 d. per yard ? XLV. THE DOUBLE RULE of THREE, In VULGAR FRACTIONS. PREPARE the numbers, as before directed, and then proceed as in page 74. EXAMPLES. (1) What principal, put to interest, will gain 41. 158. in 9 months, at 61. per cent. per annum ? (2) Suppose 12 students spend 141. 6s. 8d. in 16 days, how much will 18 students spend in 34 days? (3) If the carriage of 40 cwt. 30 miles, cost 161. 138. 4d. what weight may I have carried 80 miles for 61. 178. 6d. at the same rate? (4) Six men with their wives, upon calculation, found that their expenses for three months past (allowing 30 days to one month) amounted to 261. 19s. 4d. I demand in what time 141. 15s. may be spent by 36 men in the like proportion. (5) If 30 men can perform a piece of work in eleven days, how many will accomplish another four times as large in one fifth of the time? (6) Agreed for the carriage of 24 tons of goods, 3 miles wanting to, for of of a guinea. What was that per cwt. for a mile? 14 I : QUESTIONS for Exercise in FRACTIONS. (1) FOUR figures of nine may be so placed and disposed of as to denote and read for 100, neither more nor less. Pray how is that to be done? (2) What number is that, to which if it of 48 of 11 be added, the total will be 1? (3) What number is that, from which if you deduct the n's of Į, and to the remainder add to of 47, the sum will be 3 ? (4) What number is that, to which if you add 1 of 12, more to of 27, and from the total subtract } of7] less of 11, the remainder shall be 8? (5) There is a number, which, if multiplied by of ý of 2], will produce no more than 1, What is the cube of that number? (6) There is a number, which, if divided by sofi will quote 9 What is the square of that number? (7) If off of į of a ship be worth of ý of 1 of the cargo, value at 12001. what did both ship and cargo stand the owners in! (8) A person was possessed of a j share of a copper mine, and sold of his interest therein for 17101. what was the reputed value of the whole property at the same rate ? (9) A father devised 34 of his estate to one of his aná of the residue to another, and the surplus to his relict, for her life; the children's legacies were found to be 2571. 3s. 4d. different. Pray what money did he leave the widow the use of? sons, (10) A person, making his will, gave to one child & of his estate, to another; and when these legacies came to be paid, one turned out 5401. 10s. more than the other. What did the testator die worth? (11) A lad, having 4000 nuts, in his return home was met by Mad Tom, who took from him í of sof his whole stock. Paving Ned afterwards forced of of the remainder from him; unluckily Positive Jack found him, and required to of tz of what he had left. Smiling Dolly was, by promise, to have t of a quarter of what nuts he brought home. How many then had the boy left? (12) A younger brother received 22001. which was just 1 of his eldest brother's fortune; and 3 and į times the elder's money was į as much again as the father was worth. What was that ? (13) In distress at sea, they threw out 17 hhds. of sugar, worth 341. per hhd.; the worth of which came to but 4 of the indigo they cast overboard: besides which, 속 they threw out 13 iron guns worth 181. 10s. a-piece; the value of all amounted to } of is of that of the ship and lading. What part of the value came into (14) If A. having s of is of the half of a trading sloop and cargo, worth 16131 gl., sells his brother B. of of his interest therein at prime cost; what did it cost the brother, and what did his cousin P. pay at the same time for of the remainder? 옵 (15) X. Y. and Z. can, working together, complete a stair case in 12 days; 2. is able to do it alone in 24 days, and X. in 34. In what time then could Y. get it done himself? (16) A father dying left his son a fortune, io of which he ran through in six months; of the remainder Jasted him a twelvemonth longer, at which time he had barely 3481. left. What did his father bequeath him? (17) Kitty told her brother George that though her fortune on her marriage took 193121. out of the family, it was but of two years' rent. Pray what was it? (18) A merry young fellow in a short time ran through } of his fortune ; by advice of his friends he then gave 22001. for an exempt's place in the guards; his port? a a profusion continued till he had no more than 880 guineas left, which he found by computation was just to part of his money after the commission was bought. What was his fortune at first? (19) A person dying, left his wife with child, and making his will, ordered, that if she went with a son, y of the estate should belong to him, and the remainder to his mother; and, if she went with a daughter, he appointed the mother s, and the girl . But it happened that she was delivered both of a son and daughter; by which she lost in equity 2000l. more than if she had had only a girl. What would have been her dowry, had she only had a son ? (20) A cistern holds 103 gallons; and being brim-full, has two cocks to run off the water: by the first of which a three-gallon pail will be filled in 60 seconds, by the other in 75. In what time will this cistern be emptied through both these apertures together, supposing the efflux of the water all the same ? (21) A person having about him a certain number of crowns, said, if itits of what he had were added together, they would make just 45. How many crowns had he about him? (22) A gentleman has an orchard of fruit-trees, one half of the trees bearing apples, one fourth pears, one sixth plums, and fifty of them bearing cherries. fruit-trees in all grow in the said orchard ? (23) A schoolmaster being asked how many scholars he had, answered, if I had as many, and į as many, and as many, I should have 99. How many had he? (24) In the year I wrote this, if to my age you add * }, } (thereof), with more, The number 74 will then be had Ingenjous youths, my age explore. (25) A. in a scuffle, seized on of a parcel of sugar-plums; B. catched is of it out of his hands, and C. laid hold on } more; D. ran off with all A. had left, except }, which É. afterwards secured slily for himself; ihen A. and C. jointly set upon B., who, in the conflict, shed he had, which were equally picked up by D. and E. who laid perdue. B. then kicked down How many |