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159, 160, MISCELLANEOUS.
109 MISCELLANEOUS. 159. 1. How many seconds | ed to the same denomination, in 28 years of 365d. 6h. each ? and add them together for a
Ans. 883612800. divisor-the quotient will be 2. How many seconds from the number of times required. the birth of Christ to the end | 6. In £33 how many guinof the year1824, allowing | eas, pounds, dollars and shil365d. 5h. 48m. 57s. to a year?lings, of each an equal number? Ans. 57559853088.
Ans. 12. 3. How many seconds in 8s. 7. A person wishes to draw 120 14' 26"?" Ans. 908066. | off a hogshead of wine into gal
4. How many inches from lon bottles, two quart, quart Montpelier to Burlington, it and pint bottles, of each an being 38 miles ?
equal number; how many Ans. 2407680. | must he have? 160. 5. Three men carried in Ans. 33 bot. of each kind, 91bu, of potatoes in baskets; 1 and 9pts. over. one carried lbu. 2pk. one lbu. 1 8. If 4 men spend, each 145.. and the other 3pk. at a time, I ld. at a tavern, what is the and they all went an equal whole bill? Ans. £2. 16s. 4d. number of times; how many 9. What will be the weight 4 times did they go ?
1 of 12 silver cups, each weigh
ing llb. loz. 20 grains ? Ibu. 2pk.=6pk. As they alto 10. What will 700 bushels lbu. = 4 gether carried 13 l of potatoes cost at 1s. 3d. a 3pk.=3 pks. each time,
bushel ? Ans. £43. 15s. they evidently 13p went as many
! 11. How much wood in 27 91.
times as there are loads, each containing I cord times 13 in 91 bu. | 18ft.? Ans. 30cor. 102ft.
after being redu- 12. If 4 men spend at a tav13 ) 364 (28 times ced to pecks, i. e. in 364pks, which
ern £2 16s. 4d. what must we find by divid. each pay? 104
ing to be 28 times. 13. If 12 silver cups weigh 104 Hence
13lb. loz. 2pwt. what is the
weight of each cup? When it is required to find
14. If 700bu. of potatoes cost how many times several quan-1
1 £43 15s. what is that a bushtities, taken one of each at a i el
el? time, may be had in a given
15. If 27 loads contain 30 quantity :
cor. 102ft. of wood, how much Rule.-Reduce the given | in each load ? quantity to the lowest denom- 16. If a person travel 24rd. ination mentioned for a divi- | 12ft. in a minute, how far deod: reduce one of each of would he go, at that rate, in 2 the other quantities mention. | hours ?
17. If a man drink a pint of | 26. In 470 boxes of sugar, rum a day, how much will be each 261b. how many cwt.? drink in a year?
i Ans. 109cwt. Oqrs. 121b. Ans. 45gal. 2qt. 1 pt. 1 27. If cigars cost one and a 18. How many barley corns | half cent each, and a person will reach round the world, smoke 3 cigars per day, how supposing it to be 25020 much will it cost him for cimiles ? Ans. 4755801600. i gars during the months of Jan.
19. Divide $120 among 4 uary, February and March, in men, so that the shares shall | a common year? be to one another as 1, 2, 3, 4. Ans. 405 cents, or $4 5cts,
Ans. 12, 24, 36, 48. i 28. What is the difference 20. How many steps of 2 between six dozen dozen and feet 6 inches, must a man take half a dozen dozen ? in going from Burlington to
Ans. 792. Boston, it being 190 miles ? 29. What is the differenee
Ans. 401280 steps. between half a solid foot and, 21. If a person travel 12mi. | a solid half foot ?
16 28rd, in 2 hours, how far does YS A ns. 648 inches he go in a minute ?
30. A note was on interest 22. How many lots, each from March 20, 1819, till Jan. containing three quarters of 26, 1824; what was the length an acre, are there in a square of time? mile?
Ans. 4y. 10mo. 6d. Ans. 853 lots, and 40 rods
1 31. Divide 5 guineas among over. 23. If a vintner be desirous |
8 men-give A. 8d. more than
B. and B. 8d. more than C. &c. to draw off a pipe of wine into
what does H. receive ? bottles containing pints, quarts
Ans. 15s. 2d. H's share. and 2 quarts, of each an equal number, how many must he |
32. A horse is valued by A. have? Aps. 148 of each at $60, by B. at $69 50, and ;
24. There are three fields, 1 by C at $72 25; what is the one containing 7 acres, anoth- average judgment ! er 10 acres, and the other 12
ther 10 A. 1 $60
B. 1 69 50 The average in this acres and 1 rood; how many c. 1 72 25 case is evidently found shares of 76 rods each are
-- by dividing the sum contained in the whole ?
3) 201 75 of the sever Ads. 61 shares, and 44 rods
- ments by the number отег.
Ans. $67 25 of appraisers. 25. In 172 moidores at 36s. 33. M, N, O, and Papprais. each, how many eagles, dollars ed a ship as follows, viz. Mat and nine-pences, of each an! $6700, N at $9000, 0 at $8750, equal number?
I and P at $7380 ; what is the Ans. 92 of each, and 68pide average judgment? pences over.
Aps. $7957 50.
34. In 5529600 cubic inch. | said C should pay D $55; but es, how many cords of wood ? R said D should pay C $25;
Ans. 25 cords. how was the matter settled ? 35. A and B wishing to swap
Ans. C pays D $50. horses, and disagreeing as to 37. What is the weight of the conditions, referred the 4hhd. of sugar, each weighing matter to three disinterested 7cwt. 3qrs. 1916. ? persons, X, Y, and Z, whose Ans. 31cwt. 2grs. 20lb. judgments were as follows, viz. 38. Three men and 2 boys X said A should pay B $8, and hoed 30000 hills of corn, and Y said A should pay B $6; but each man hoed two hills while Z said B should pay A $5; a boy hoed one; how many hills what is the average judgment were hoed by each man, and
Ans. A must pay B $3. how many by each boy?
A B In the exchange of ar Ans. Each man hoed 7500, x 1.90 98 ticies, where the judg. ! and each boy 3750 hills. Y 1. 0° 6 ment of the referees is |
3X2+2=8 Divisor. 2 1. 5 O partly on one side of
39. If $911.555 be divided - -.- the equality between Ref. 3 5 14 them, and partly on among 5 men and 4 women,
14 B the other, subtract one | what is each man and woman's
and divide the remain. I double that of a woman?
Anel $65.111=wom's share. 36. C and D wishing to swap
$ $130.222=man's share. farms, referred the subject to i
40. Two places differ in lonO. P. O and R, and agreed to gitude 31° 37' 3"; what is their abide their judgment, which ! difference in reckoning time, was as follows, viz. O said C | allowing 15° to make an hour? should pay D $70; P said C
Ans. 2h. 6' 282". should pay D $100; and Q
REVIEW 1. When are numbers called | 7. How is the year commonly dicompound, or complex?
| vided ? Repeat the number of days 2. By what are the operations per- in each month. formed by compound numbers regu- 8. What is meant by leap year? lated ?
how may we know whether a year 3. Repeat the table of Federal | is leap year or not? What is meant money, -of English money. ! by old and new style?
4. What are the names and val. | Let the pupil be questioned in like ues of the coins of the United manner respecting the other laStates?
bles. 5. What are the most common ! 9. What is Reduction ? Of bow foreign coins? what their several many kinds is it? values?
10. What is the rule for Reduc6. What is the table of time? Ition Descending? Ascending?
11. What is the method of proof 18. If you wish to subtract one in each?
date from another, how would you 12. How would you proceed to proceed? (152) naultiply by 5%? to divide by 54 ? 19. What is Compound Multi
13. What is meant by Reduction plication ?-lhe Rule? What is · of Decimals?
Compound Division ?-the Rule ? 14. How would you proceed to What relation have these two rules find the value of a decimal in inte to each other? Of what contracgers of a lower denomination? Howtions are these rules susceptible? to reduce compound numbers to de. 20. What are the several concimals of a higher denomination ? tractions of Simple Multiplication ?
15. How many days are com (90, 91, 92, 93,) – of Divisiou? (103, monly reckoned to a month, in com 109, 110, 111.) puting interest ? (145) How are 21. What is meant by a simple days and months reduced to a deci- ! number? What is the distinction mal of a year?
| between a simple and a compound ? 16. What is Compound Addition? 22. How would you proceed to --the Rule?-Proof?
take quantities of several denomi. 17. What is Compound Subtrac | nations, each an equal number of tion ?--the Rule?-Proof?
| times, from a given quantity?
161. Per Cent. is a contraction of per centum, Latin, signifying by the hundred, and implies that calculations are made by the hundred. Per Annum signifies by the year.
ANALYSIS. 162. If I lend a neighbor 25 dollars for one year, and he allow me 6 cents for the use of each dollar, or 100 cents, how much must he pay me in the whole at the end of the year?
1 If he pay 6 cts.=.06 of a dollar (132) for the use of 100 .06 cts, or i dollar, he must evidently pay 25 times .06, or (86)
.06 times 25=$1.50 for the use of 25 dollars. Hence, 1.50 25-+-1.50–$26.50 is the sum due me at the end of the 25. year. The $25 is called the principal, the .06 is called
the rate percent. the $1.50 is called the interest, and the 26.50 - $26.50 is called the amount. Hence the following
DEFINITIONS. 163. Interest is a premium allowed for the use of money. The sun of money upon interest is called the principal.
The rate is the per cent. per annum agreed on, or the inte. rest of one dollar for one year, expressed decimally.
164, 165, 166, 167, SÍMPLE INTEREST.
113 The principal and interest added together are called the amount.
Interest is of two kinds, Simple and Compound.
164. The rate per cent. is expressed in hundredths of a dollar. Decimals in the rate below hundredths are parts of one per cent. The rate of interest is generally established by law. In New-England legal interest is 6 per cent. in New York 7 per cent, and in England 5 per cent. Where the rate is not mentioned in this work, 6 per cent. is understood. '
165. Simple Interest is that which is computed on the principal only.
ANALYSIS. 166. 1. What is the interest of 838.12 for 2 years, 8 munths and 21 days, at 6 per cent. per annum?
$38.12 .Multiplying the principal by the rate gives the in.06 terest for one year, (161) and the interest for one year
multiplied by the number of years, is evidently the jo$2.2872 terest for the whole time. Twenty-one days are şi 2.725 of a month=0.7, and 8 mo. 21d.=8.7 mo. But months
are 12ths of a year, hence 8.7m=mo.=0.725 year, 114360 (142) and 2yr. 8mo. 210.=2.725 years, we therefore
45744 multiply 2.2872, the interest for one year, by 2,725, the 150104 number of years, and the product. $6.132, is the inter45744 est for the whole time. Hence,
167. To compute the interest on any sum for any time. Rule. Multiply the principal by the rate, expressed as a decimal of a dollar, and the product will be the interest for one year. Multiply the interest thus found by the number of years, (reducing the months and days, if any, to the decimal of a year) .(145) and the product properly pointed (106, 116) will be the interest required.
Note.-In solving the following questions, the decimal of a year, when it has not terminated sooner, has been carried to four places of figures, and that will give the interest sufficiently correci for common practice. When great accuracy is required, find the number of days in the given months and days, and divide these by 365, the number of days in a year and the quotient will be the true decimal of a year.