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2. Having reduced the Fractions, and stated the Question, as before directed;

3. Multiply the Denominator of your first Number into the Numerators of the second and third, for a new Numerator; then multiply the Numerator of the first Number into the Denominator 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 23 Yards of Silk cost 331. what will 44 Yards cost at the same Rate?

(2) If of a lb. cost 5s 6d. what will 423 lb. of the same

cost?

(3) Suppose I give 14s 8d. for cwt. what must be given for 8 cwt. of the same at that Rate?

(4) A Merchant makes an Assurance upon

Ship and Cargo, bound to a certain Port, Value 2700/ 10s. and agrees to pay 10 Guineas per Cent. To what comes the Premium or Charges of the Assurance?

(5) How much South-Sea Stock, at 1127. per Cent. will 1270% purchase?

(6) A Mercer bought 44 Pieces of Silk, each Piece contain

ing 223 Yards, and was to give 8s 9d. per Yard. I demand the Value of the whole?

(7) If I give 100/ 10s 6d. for 12 Pieces of Holland, at the Rate of 5s 6d. per Ell Flemish ; I demand how many Ells 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.

EXAMPLES.

(1) A. lends B. 2547. for 6 Months. How long ought B. to let A. have 1047. to requite his Kindness ?

(2) If 4 Men can do a Piece of Work in 123 Hours, in how many Hours will 12 Men do the same?

(3) If the Penny Loaf weighs 123 oz. when the Bushel of Wheat is sold for 5. what is the Load worth when the Penny Loaf weighs 8 oz.?

(4) Suppose A. lends to B. 1003/. for 63 Months, what Sum must B. lerd A. for 3 Years, to requite him? (5) How many Yards of Cloth, at 8s 6d. per Yard, must be given for 26 Yards, at 5s 7d. per Yard?

XLV. The DOUBLE RULE of THREE,

IN VULGAR FRACTIONS.

RULE.

PREPARE the Numbers as before directed, and then proceed as in page 74.

EXAMPLES.

(1) What Principal, put to Interest, will gain 4/ 15s. in 9 Months, at 61. per Cent. per Annum?

(2) Suppose 12 Students spend 147 6s 8d. in 16 Days, how much will 18 Students spend in 34 Days?

(3) If the Carriage of 40 cwt. 30 Miles, cost 167 13s 4d. what Weight may I have carried 80 Miles for 6/ 178 6d. at the same Rate?

(4) Six Men with their Wives, upon Calculation, found that their Expences for three Months past (allowing 30 Days to one Moath) amounted to 26/ 19s 4d. I demand in what Time 14/ 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 big in one Fifth of the Time!

(6) Agreed for the Carriage of 2 Tons of Goods, 3 Miles wanting for 4 of 3 of a Guinea. What was that per cwt. for a Mile?'

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 3 of 3 of 141 be added, the Total will be 1?

(3) What Number is that, from which if you deduct the of, and to the Remainder add of 43, the Sum will be 3?

(4) What Number is that, to which if you add

of 12, more of 27, and from the Total subtract of 71⁄2 less of 14, the Remainder shall be 8?

(5) There is a Number, which, if multiplied by of of 23, will produce no more than 1. What is the Cube of that Number?

(6) There is a Number, which, if divided by 3 of 3 will quote 9. Pray what is the Square of that Number?

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(7) If 3 of # of of a Ship be worth of of of the Cargo, Value at 12007, what did both Ship and Cargo stand the Owners in ?

(8) A Person was possessed of a 3 Share of a Copper Mine, and sold of of his Interest therein for 1710. What was the reputed Value of the whole Property at the same Rate?

(9) A Father devised 14 of his Estate to one of his Sons, and 4 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?

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(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 540/ 10s. more than the other. What did the Testator die worth? (11) A Lad having got 4000 Nuts, in his return home was met by Mad Tom, who took from him of 3 of his whole Stock. Raving Ned lighted on him afterwards, and forced of of the Remainder from him; unluckily Positive Jack found him, and required of 12 of what he had left. Smiling Dolly was, by Promise, to have 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

of his elder Brother's Fortune; and 3 and Times the elder's Money was as much again as the Father was worth. What was that?

(13) In Distress at Sea, they threw out 17 hhds. of Sugar, worth 347. per hhd.; the Worth of which came up to but of the Indigo they cast overboard: besides which, they threw out 13 Iron Guns worth 18/ 10s. a-piece; the Value of all amounted to off of that of the Ship and Lading. Pray what Part of the Value came into Port?

(14) If A. having of of the Half of a trading Sloop and Cargo, worth 161317. 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?

(15) X. Y. and Z. can, working together, complete a Staircase in 12 Days; Z. is Man enough to do it alone in

24 Days, and X. in 34.

Y. get it done himself?

In what Time then could

(16) A Father dying left his Son a Fortune,

of which he ran through in 6 Months; of the Remainder held him a Twelvemonth longer, at which Time he had bare 3481. left. Pray 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. Heaven be praised for this yearly Income! Pray what was it? (18) A merry young Fellow; in a short Time got the better of of his Fortune; by Advice of his Friends he then gave 22001. for an Exempt's Place in the Guards; his

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Profusion continued till he had no more than 880 Gui-
neas left, which he found by Computation was just
Part of his Money after the Commission was bought.
Pray 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, of the Estate should belong to him, and the Remainder to his Mother; and, if she went with a Daughter, he appointed the Mother, and the Girl . But it happened that she was delivered both of a Son and Daughter; by which she lost in Equity 20007. 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 4++ 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. How many 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 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

I

,,, (thereof), with more,

The Number 74 will then be had.

Ingenious Youths, my Age explore.

(25) A. in a Scuffle, seized on of a Parcel of Sugar-Plums B. catched of it out of his Hands, and C. laid hold on more; D. ran off with all A. had left, except

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, which E. afterwards secured slyly for himself; then 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

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