Arithmetic, Part 1 · Section 34

Arithmetic · Part 1 · Section 34

p. 120The Rule of Fellowſhip with time.

THis Rule is to be uſed when the times of the continuance of the particular ſtocks are unequal, and differ; ſo that here the difference of time, and alſo the difference of ſtock being both to be conſidered; it can be done no better way then by taking the Power of them both to be the particular ſtock; and all thoſe Powers added, to be the whole ſtock, that which I call the Power, is the product of the money of every one multiplyed by his time; And then

THE RƲLE.

As the ſumme of thoſe Products, is to the whole gain; ſo is each particular product, to its part of the gain.

Queſtion 1.

Three Merchants A. B. C. make a ſtock of 10000 l. of which A layes in 4000 for 3 moneths, B. 3000 l. for 6 moneths; and C. 3000 l. for 8 moneths, with this they gain 2000 l. what is each mans ſhare?

p. 121Firſt, for A. multiply 4000 by 3, it makes 12000, let that be accounted his particular ſtock.

Secondly, for B. multiply 30000 by 6, it makes 18000.

Laſtly for C. multiply 3000 by 8, it produceth 24000, for his ſtock, adde theſe, they make 54000 l. for the general ſtock; then ſay,

For A.

If 54000 give 2000, what 12000? anſwer, 666 24000/54000.

Then for B.

If 54000 give 2000, what 18000? anſwer 444 36000/54000.

Laſtly, for C.

If 54000 give 2000, what 24000? anſwer, 888 48000/54000.

The three Fractions may be reduced (by dividing each Numerator, and Denominator by 6000) and then the three ſhares will be 444 4/9, 66 6/9, and 888 8/9, which altogether make 2000, as they ought.

Queſtion 2.

Three Farmers, A. B. and C. lay out 1000 l. to ſtock their grounds with Cattel, of which A. put in 200 l. for 6 yeares; B. had 300 l. going for 4 yeares; and C. 500 l. for 2 years; at the end (by unſeaſonable times) there was loſt 200 l. which made the remain of their ſtock but 800 l. what had each man left?

Multiply 200 by 6, it gives 1200: Likewiſe, 300 by 4, it gives 1200. Laſtly, 500 by 2, the product is 1000: all theſe are 3400 for the joynt ſtock.

p. 122Then firſt for A.

Say, if 3400 loſe 200, what 1200? anſwer, 70 2000/3400 for A, to which B is equal, becauſe the power of his ſtock is ſo.

Therefore for C.

Say, if 3400 loſe 200, what 1000? anſwer, 58 2800/3400. So the 3 ſhares are 70 20/34, 70 20/34, and 28 2…/34, equal to 200.

Now becauſe A put in 200 l. and loſt 70 20/34 ſubtract the loſſe from the ſtock, remains 129 14/34.

And ſo doing for B, his remain will be 289 14/34.

And for C, his remain is 441 6/34. Now theſe three remains, 129 14/34, 229 14/34, and 441 6/34, make up 800 l. which was the whole remain.

Queſt. 3.

A. rents a cloſe for a year, to pay 80 l. he puts into it 200 ſheep: 2 months after B. puts 40 ſheep in; and 5 moneths after that C. puts in 100 ſheep; how much muſt every one pay of the rent?

Then for A.

If 3300 pay 80, what 2400? anſwer, 58 600/3300.

Then for B.

If 3300 pay 80, what 400? anſwer, 9 2300/3300.

And for C.

If 3300 pay 80, what 500? anſwer, 9 400/3300.

The whole numbers make 79, and the broken numbers make 1. In all 80.

p. 123Note

Whereas, hitherto we have conſidered onelyonly difference of time and money; it may be noted, that there may be difference of other kinds, as perſons or place; but whatſoever they are the power of all is found like theſe by multiplication; and are to be worked like theſe, with ſo many Uſes of the Golden Rule, as the queſtion requires. I will therefore adde but one queſtion more, which is this.

Queſt. 4.

One leaves a Legacy of 900 l. among foure Kinsfolks. A. B. C. D; ſo as B may have twice as much as A. and C thrice as much as B. and D as much and half as much as C, what is every one to have.

Say, if A be 1, B is 2, C 6, and D 9, adde theſe Numbers: 1, 2, 6, 9, together, they give 18, then ſay, If 18 require 900, what 1? anſwer is 50. So A is to have 50 l. B 100 l. C 3000 l. and D 450 l. which are their juſt parts; and altogether are equal to 900 l. and the work right.