« PreviousContinue »
32. What part of 25 is of an unit ? 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. 54 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 1, in the third }, in the fourth i'ī, and in the fifth 450 ; how many had he ?
Ans. 1200. 35. A and B together can build a boat in 18 days, and
a with the assistance of C tliey can do it in 11 days; in what time would C do it alone? Ans. 284 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 57. 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. SS. If 3 dozen pairs of gloves be equal in value
to 2 pie ces 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 inay be bought for 288.?
Ans. 2 dozen puirs. 39. A lets B have a hogshead of sugar of 18 cwt. worth 5 dollars, for 7 dollars the cwt. 1 of which he is to pay in cash. B hath påper worth 2 dollars per ream, which he gives A for the rest of his sugar, at 2. dollars per rean.. Which gained most by the bargain?
Ans. A by $19, 20cts. 40. A father left his two sons (the one 11 and the other 16 years old) 10000 dollars, to be divided, so that each share, being put to interest at 5 per cent. might amount to equa! sums when they would be respectively 21 years of age. Required the shares ?
Ans. 5454,41 and 454541 dollars. 41. Bought a certain quantit: of broadcloth for 3831
5s. and if the number of shillings which it cost per yard were added to the number of yards bought, the sum would De 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 183. 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 inuch: 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 şays to John, My part of the gain is really a handsome sum of money ; I wish I had as many such sums
1 as your part contains dollars, I should then have S960000. I demand each man's particular stock in purchasing the goods.
Ans. Peter paid 600 dollars, and John paid 400.
SURVEYORS. 1. Required to lay out a lot of land in form of a long square, containing 3 acres, 2 roods, and 20 rods, that shalt 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 YI. page 189. 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 fails 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,
rail shall fence an acre ?
contains 256000 acres. Thus, 1 mile=320 rods : then 320X320-:-160=640 acres : and 320 X4x10=12800 rails. As 640 : 12800 :: 12800 : 256000 rails, which will enclose 256000 acres 20 miles square.
JOR FINDING THE CONTENTS OF SUPERFICIES, SOLIDS,
SHORT RULES, FOR CASTING INTEREST AT SIX PER CENT 1. 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 tiree 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 ncarly.
Ans. 5d. 1,64rs. 2. What is the interest of 211. 38. for 29 days:
Ans. 2s. Od. 2grs.
FEDERAL MONEY. il. To find the interest of any number of cents for any number of days less than a month, at 6 per cent.
RULE, Multiply the cents by the number of days, divide the product by 6, and point off two figures to the right, and all the figures at the left hand of the dash, will be the interest in mills, nearly.
EXAMPLES. Kequired the interest of 85 dollars, for 20 days. 8 cts.
Ins. 283 which is
28cts. 3 mills. 2. What is the interest of 73 dollars 41 cents, or 7341 '. cents, for 27 days, at 6
III. When the principal isgiven in pounds, shillings, &c.
New-England currency, to find the interest for any number of days, less than a month, in Federal Moncy.
RULE. Multiply the shillings in the principal by the number of days, and divide the product by 36, the quotient will be the interest in mills, for the given tiinc, nearly; oinitting fractions.
EXAMPLE. Required the interest, in Federal Money, of 271. 15s. for 27 (lays, at 6
cent. £. S. Ans. 37 15=555 X 27-36=416mills.241cts, 6M.
IV. When the principal is given in Federal Moncy, anil
you want the interest in shillings, pence,&c. New-Eng. land currency, for any number of days less than a month..
RULE. Multiply the principal, in cents, by the number of daye and point off five figures to the right hand of the product, which will give the interest for the given time, in shil. lings and decimals of a shilling, very nearly.
A note for 65 dollars, 31 cents, has been on interest 25 days; how much is the interest thereof, in New-England currency? S cts.
s. d.qrs. Ans. 65,31=6531X25=1,63275=1 72 REMARKS. In the above, and likewise in the preceding practical Rules, (page 127) the interest is confined at six per cent. which admits of a variety of short methods of casting; and when the rate of interest is 7 per cent. as established in New-York, &c. you may first cast the interest at 6 per cent. and add thereto one sixth of itself,
6 and the sum will be the interest at 7 per cent. which per• haps, many times, will be found more convenient than the general rule of casting interest.
Required the interest of 751. for 5 months at 7 per not.
7,5 for 1 month,
6. s. d.
37,5=1 17 6 for 5 months at 6 perc
Ans. £? 3 9 for ditto at 7
A SHORT METHOD FOR FINDING THE REBATE OF ANY GIVEN SUN, FOR MONTHS AND DAYS.
RULE. Diminish the interest of the given sum for the time by its own interest, and this gives the Rebate very ncarly.
1. What is the rela te of 50 dollars for six months, at 6 per cent