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; cr as in Multipli

cation.

EXAMPLES.

(1) If 23 Yards of Silk cost 341. what will 44 Yards cost at the same Rate?

(2) If 3 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 a Ship and Car

go, 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 112. per Cent. will 12701. purchase?

(6) A Mercer bought 44 Pieces of Silk, each Piece containing 223 Yards, and was to give 8s 9d. per Yard. I demand the Value of the whole?

(7) If I give 1007 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. 25l. for 6 Months. How long ought B. to let A. have 1037. to requite his Kindness?

(2) If 4 Men can do a Piece of Work in 124 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 5s. what is the Load worth when the Penny Loaf weighs 83 oz.?

(4) Suppose A. lends to B. 10037 for 63 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 26 Yards, at 5s 7d. per Yard ?

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 67. 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 wt. 30 Miles, cost 16/ 13s 4d. what Weight may I have carried 80 Miles for 6! 17s

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 Month) amounted to 261 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 24 Tons of Goods, 3 Miles wanting for of 3 of a Guinea.

per cwt. for a Mile?

What was that

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

added, the Total will be 1?

of 7 of 14 be

(3) What Number is that, from which if you deduct the of, and to the Remainder add of 47, the Sum will be 3?

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

more of 27, and from the Total subtract
Less of 14, the Remainder shall be 8?

of 12,

of 71⁄2

(5) There is a Number, which, if multiplied by 3 of 1 of 23, will produce no more than 1. What is the Cube of that Number?

(6) There is a Number, which, if divided by of will quote 9. Pray what is the Square of that Number? (7) If 3 of 4 of of a Ship be worth of of of the 우 Cargo, Value at 1200%. what did both Ship and Cargo stand the Owners in?

I

(8) A Person was possessed of a 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?

4.

(9) A Father devised 34 of his Estate to one of his Sons, and 44 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?

(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 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 17 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

20

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 187 10s. a-piece; the Value of all amounted to of of that of the Ship and Lading. Pray what Part of the Value came into Port?

(14) If A. having of 3 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. In what Time then could Y. get it done himself?

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

of which he rau through in 6 Months; of the Remainder held him a Twelvemouth 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 22007. for an Exempt's Place in the Guards; his

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 2000. 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 ++ 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 Cherrics. 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.

(24)

he?

How many had

In the Year I wrote this, if to my Age you add

,,, (thereof), with more,

The Number 74 will then be nad

Ingenious Youths, my Age explore.

(25) A. in a Scuffle, seized on 3 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 , 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