10. If 10 head of cattle require 20A. 2R. of pasture ground, for a summer, how many acres ought 25 head to have, for the same time? Ans. 51A. 1R. 11. A cistern is filled with water, by 2 pipes, in 3hr. 25m. In what time would it be filled by 5 pipes of like size? Ans. 1hr. 22min.

12. A sum of money having been equally divided among 19 men, each man received $31. If the number of men had been 30, what would have been the share of each?

Ans. $2.058'. 13. Allowing 15A. 30P. to produce 403bu. 2pk. of wheat, how many bushels would be raised from a field containing 40 acres, at the same rate? Ans. 10625bu.

14. If 25 sacks, each measuring 4bu., will contain a given quantity of corn; how many sacks, each measuring 31⁄2bu., will contain the same quantity? Ans. 284 sacks.

15. A post, standing in a stream, has

of its length in

the earth, in the water, and 5 feet above the water. What is the length of the post?

ANALYSIS.

+= }}; and 1-3 = &·

The post has therefore of its length above the surface

of the water;

of its length is then 5 feet;

5 feet, and the whole length is

of it is of

15 of 5 feet = 75 = 37 feet.

The proportion in the question is, the part,, above the water, is to a unit, as the length, 5ft., of the part above the water, is to the entire length.

16. A farmer sold of his land to A, remainder, which was 100 acres, to C. the farmer own?

Ans. 37 feet. of it to B, and the How much land did

Ans. 240 acres.

17. In a certain school, of the pupils study Arithmetic, of them study Languages, and the remaining 36 are employed on various other subjects. Required the number in the school. Ans. 96 pupils.

18. A person failing in business owes $5000, and is able to pay but $2000. How much can he pay per dollar to his creditors? Ans. $0.40. 19. A traveler having gone 375.5 miles on his journey, finds that of it remains to be traveled. length of his journey?

What was the Ans. 600.8 miles.

20. A gentleman who owned of a manufactory, sold of his share for $3000. What was the estimated value of the whole establishment? Ans. $18000.

21. How many miles must a person walk in 5 days, to accomplish a journey of 500.5 miles, at the same rate, in 15 days? Ans. 183.516' miles.

22. A bankrupt owes $5349.75, and has property amounting to $2300. In an equitable distribution of his property, how much will a creditor receive whose claim is $400 ?

Ans. $171.970'.

23. A borrowed of B $500, which he kept 3 years. On a subsequent occasion A lends B $375; how long ought B to keep this latter sum in return for the accommodation he had afforded A? Ans. 4 years.

24. Allowing a man to do a certain work in 3 days, and a boy to do it in 5 days, in what time ought the two together to do the work?

ANALYSIS. The man could do, and the work, in 1 day; then both together could do the work in 1 day; hence they could do and the entire work in 15 of a day.

25. A can dig a ditch in 5 days, B in 6 days, and C in 8 days. In what time could the three together dig the ditch? Ans. 22 days.

26. If 4T. 13cwt. of iron be conveyed 50 miles for $30 how far should 9T. 5cwt. 3qr. be conveyed for the same sum ? Ans. 25.033' miles. 27. Two masons together build a wall in 10 days. One of them could have built the wall himself in 15 days; in what time could the other have done it? Ans. 30 days.

28. A merchant bought three pieces of cloth, each containing 25yd. 2qr., for $500; and sold 50yd. of it at cost. What did the 50 yards amount to? Ans. $326.79'.

29. If of of an acre of land sell for $18.183, what would a lot containing 7A. 2R. 13P. bring at that rate? Ans. $229.80'. 30. How many yards of linen which is yd. wide will be equivalent to 30 yd. of another kind which is of a yard wide? Ans. 45 yards. 31. How many yards of carpeting which is of a yard wide, will be required to cover a floor that measures 25 feet in length, and 20 feet in breadth? 32. A farmer has a field 100 poles in length, and 45.25 poles in width. He wishes to lay off another field to contain the same quantity of ground, and be 80 poles in length; what must be its breadth ? Ans. 56.5625 poles.

Ans. 74

yards.

33. The governor of a besieged place has provision for 54 days, at the rate of 16. of bread to each man per day, but is desirous to prolong the siege to 80 days, in expectation of succor; in that case what must the ration of bread be ?

Ans. 1lb. per day

PARTITIVE PROPORTION.

(147.) PARTITIVE PROPORTION is Proportion applied to dividing a given quantity into two or more parts which shall have a given ratio, one to another.

The terms of the given ratio, or ratios, may be called the proportional terms.

For example, to divide $150 into three parts which shall be to one another in the proportion of 2, 3, and 5; that is, the first part to the second as 2 to 3, and the second to the third as 3 to 5.

In this example, 2, 3, and 5 are the proportional terms.

This division of Arithmetic is commonly called PartnerSHIP or FELLOWSHIP.

RULE XXXIV.

(148.) To Divide a given Quantity into two or more parts which shall have a given Ratio, one to another.

1. Add together all the given proportional terms. Then, 2. The sum of those terms will be to any one of the terms, as the quantity to be divided, is to the part corresponding to that term.

EXAMPLE.

To divide $150 between A, B, and C in the proportion of 2, 3, and 5.

The sum of the given proportional terms is 2+3+5=10;

ANALYSIS. Suppose to the whole sum $150 to be divided into 2+3+5, or 10 equal parts; then it is evident that A must have two, B three, and C five of those parts; that is,

The results obtained by the Analysis will be the same as those obtained by the Rule.

EXERCISES.

1. Divide $240 between three persons in such a manner that their shares shall be as the numbers 5, 4, and 3.

Ans. $100; $80; and $60.

2. A gentleman divided $10000 between his son and daughter in the proportion of 3 to 2. spective shares ?

What were the reAns. $6000, and $4000.

3. A testator bequeathed $15000 to his widow, daughter, and son in the proportion of 3, 5, and 7. What were the respective shares? Ans. $3000; $5000; and $7000.

4. A merchant employed three clerks at the annual salaries of $300, $400, and $500. At the end of the year, having become bankrupt, he has but $650 to be divided proportionally among them. What will be the portion of each?

The proportional terms are 300, 400, and 500; or, without altering the ratios, 3, 4, and 5, since 3883, and 400. Ans. $162.5; $216.66'; and $270.83'.

5. An insolvent debtor owes to A $250, to B $100, and to C $300. He is able to pay $420; what should each of the three creditors receive?

Ans. $161.538'; $64.615'; and $193.846'.