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15. A young man received 2107. which was of his elder brother's portion; now three times the elder brother's portion was half the father's estate; what was the value of the estate ? Ans. £1890. 16. A hare starts 40 yards before a grey-hound, and is not perceived by him till she has been up 40 seconds; she scuds away at the rate of ten miles an hour, and the dog, on view, makes after her at the rate of 18 miles an hour: How long will the course hold and what space will be run over from the spot where the dog started?

Ans. 60

sec. and 530 yds. space. 17. What number multiplied by 57 will produce just what 134 multiplied by 71 will do? Ans. 166.

18. There are two numbers whose product is 1610, the greater is given 46; I demand the sum of their squares, and the cube of their difference?

Ans. the sum of their squares is 3341. The cube of their difference is 1331.

19. Suppose there is a mast erected, so that of its length stands in the ground, 12 feet of it in the water, and of its length in the air, or above water; I demand the whole length? Ans. 216 feet.

20. What difference is there between the interest of 5007. at 5 per cent. for 12 years, and the discount of the same sum at the same rate, and for the same time?

Ans. £112 10s.

21. A stationer sold quills at 11s. per thousand, by which he cleared 3 of the money, but growing scarce raised them to 13s. 6d. per thousand; what might he clear per cent. by the latter price? Ans. £96 7s. 3 d.

22 Three persons purchase a West-India sloop, towards the payment of which A advanced 3, B, and C 1407. How much paid A and B, and what part of the vessel had C?

Ans. A paid £267f1, B £305†, and C's part of the vessel was

23. What is the purchase of 12007. bank stock, at 103 Ans. £1243 10s. per cent.? 24. Bought 27 pieces of Nankeens, each 11 yards, at

14s. 44d, a piece, which were sold at 18d. a yard; required the prime cost, what it sold for, and the gain.

25. Three partners, A, B and C, join their stock, and buy goods to the amount of £1025,5; of which A put in a certain sum; B put in...I know not how much, and C the rest; they gained at the rate of 241. per cent.: A's part of the gain is, B's, and C's the rest. Required each man's particular stock.

A's stock was 512,75

26. What is that number which being divided by 3, the

quotient will be 21?

27. If to my age there added be,

One-half, one-third, and three times three,
Six score and ten the sum will be;

What is my age, pray show it me?

Ans. 153.

Ans. 60.

28. A gentleman divided his fortune among his three sons, giving A 97. as often as B 51. and to C but 31. as often as B 77. and yet C's dividend was 25847.; what did the whole estate amount to? Ans. £19466 25, Ed.

29. A gentleman left his son a fortune, of which he spent in three months; of the remainder lasted him 10 months longer, when he had only 2524 dollars left; pray what did his father bequeath him? Ans. $5889, 33cts.+.

30. In an orchard of fruit trees, of them bear apples, pears, plums, 40 of them peaches, and 10 cherries: how many trees does the orchard contain? Ans. 600.

31. There is a certain number which being divided by 7, the quotient resulting multiplied by 3, that product divided by 5, from the quotient 20 being subtracted, and 30 added to the remainder, the half sum shall make 65; can you tel me the number? Ans. 1400.

32. What part of 25 is § of a unit?

Ans.

33. If A can do a piece of work alone in 10 days, B in 20 days, C in 40 days, and D in 80 days; set all four about it together, in what time will they finish it? Ans. 5} days.

34. A farmer being asked how many sheep he had, answered, that he had them in five fields; in the first he had of his flock, in the second, in the third, in the fourth , and in the fifth 450; how many had he? Ans. 1200. 35. A and B together can build a boat in 18 days, and with the assistance of C they can do it in 11 days; in what time would C do it alone? Ans. 282 days.

36. There are three numbers, 23, 25, and 42; what is the difference between the sum of the squares of the first and last, and the cube of the middlemost? Ans. 13332.

37. Part 1200 acres of land among A, B, and C, so that B.may have 100 more than A, and C 64 more than B. Ans. A 312, B 412, C 476.

33. If 3 dozen pairs of gloves be equal in value to 2 pieces of Holland, 3 pieces of Holland to 7 yards of satin, 6 yards of satin to 2 pieces of Flanders lace, and 3 pieces of Flanders lace to 81 shillings; how many dozen pairs of gloves may be bought for 28s. ? Ans. 2 dozen pairs.

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39. A lets B have a hogshead of sugar of 18 cwt., worth 5 dollars, for 7 dollars the cwt. of which he is to pay in cash. B hath paper worth 2 dollars per ream, which he gives A for the rest of his sugar, at 2 dollars per ream; which gained most by the bargain? Ans. A by $19 20 cts.

40. A father left his two sons (the one 11 and the other 16 years old) 10,000 dollars, to be divided so that each share being put to interest at 5 per cent. night amount to equal sums when they would be respectively 21 years of age. Required the shares? Ans. 5454, and 4545 dollars.

41. Bought a certain quantity of broadcloth for 3837,

5s. and if the number of shillings which it cost per yard were added to the number of yards bought, the sum would be 386; I demand the number of yards bought, and at what price per yard? Ans. 365 yds. at 21s. per yard. Solved by PROBLEM VI. page 171.

42. Two partners Peter and John, bought goods to the amount of 1000 dollars; in the purchase of which, Peter paid more than John, and John paid.....I know not how much: They then sold their goods for ready money, and thereby gained at the rate of 200 per cent. on the prime cost: they divided the gain between them in proportion to the purchase money that each paid in buying the goods; and Peter says to John, My part of the gain is really a handsome sum of money; I wish I had as many such sums as your part contains dollars, I should then have $960,000. I demand each man's particular stock in purchasing the goods. Ans. Peter paid $600 and John paid $400.

THE FOLLOWING QUESTIONS ARe proposeD TO SURVEYORS:

1. Required to lay out a lot of land in form of a long square, containing 3 acres, 2 roods and 29 rods, that shall take just 100 rods of wall to enclose, or fence it round; pray how many rods in length, and how many wide, must said lot be? Ans. 31 rods in length, and 19 in breadth,

Solved by PROBLEM VI. page 171.

2. A tract of land is to be laid out in form of an equal square, and to be enclosed with a post and rail fence, 5 rails high; so that each rod of fence shall contain 10 rails. How large must this noble square be to contain just as many acres as there are rails in the fence that encloses it, so that every rail shall fence an acre?

Ans. the tract of land is 20 miles square, and contains 256,000 acres.

Thus, 1 mile=320 rods: then 320×320-160=640 acres and 320 4 × 10-12,800 rails. As 640: 12,800 : : 12,800: 256,000, rails, which will enclose 256,000 acres== 20 miles square.

AN

APPENDIX,

CONTAINING

SHORT RULES,

FOR

CASTING INTEREST AND REBATE;

TOGETHER WITH SOME

USEFUL RULES,

FOR FINDING THE CONTENTS OF SUPERFICES, SOLIDS, &c.

SHORT RULES,

FOR CASTING INTEREST AT SIX PER CENT. I. To find the interest of any sum of shillings for any number of days less than a month, at 6 per cent.

RULE.

1. Multiply the shillings of the principal by the number of days, and that product by 2, and cut off three figures to the right hand, and all above three figures will be the interest in pence.

2. Multiply the figures cut off by 4, still striking off three figures to the right hand, and you will have the farthings, very nearly.

EXAMPLES.

1. Required the interest of 51. 8s. for 25 days.

5,8=108× 25×2=5,400, and 400 × 4=1,600.

Ans. 5d. 1,6qrs.

2. What is the interest of 217. 3s. for 29 days?

Ans. 2s. Od. 2 qrs.