MISCELLANEOUS. 159. 1. How many seconds | ed to the same denomination, a 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 year 1824, allowing eas, pounds, dollars and shil365d. 5h. 48m. 57s. to a year? lings, of each an equal numAns, 57559853088. ber? Ans. 12. 3. How many seconds in 8s. 7. A person wishes to draw 12° 14' 26" ? Ans, 908066. off a hogshead of wine into 4. How many inches from gallon bottles, two quart, quart Montpelier to Burlington, it and pint bottles, of each an being 38 miles ? equal number; how many must Ans. 2407680. he have ? 160, 5. Three men carried Ans. 33 bottles of each kind, in 91bu. of potatoes in baskets; and 9pts. over. one carried Ibu, 2pk. one lbu. 8. If 4 men spend each 14s. and the other 3pk. at a time, 1d. 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 times did they go ? of 12 silver cups, each weig) ing llb. loz. 1pwt. 20 grains ? 1 bu. 2pk.pk. As they alto- 10. What will 700 bushels 1 bu. gether carried 13 of potatoes cost, at 1s. 3d. a bushel ? Ans. £43 15s. 11. How much wood in 27 Ans. 30cor. 102ft. after being re13)364(28 times duced to pecks, 12, If 4 men spend at a tava ern £2 16s. 4d., what must dividing, to be 28 13. If 12 silver cups weigh 13]b. loz. 2pwt., what is the weight of each cup ? When it is required to find 14. If 7000u. of potatoes cost now many times several quan- £43 15s, what is that a bushtities, taken one of each at a 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- 6. If a person travel 32rd. imation mentioned for a divi-, 3ft . 10 in, in a minute, how dend: reduce one of each of far would he go, at that rate, the other quantities mention in 2 hours ? 26 160. MISCELLANEOUS. 56 17. If a man drink a pint of 26. In 470 boxes of ougar, rum a day, how much will he each 261b., how many cwt. ? drink in a year? Ans. 109cwt. Oqrs. 121b. Ans. 45gal. 2qt. 1pt. 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 cigars miles ? Ans. 4755801600. during the months of January, 19. Divide $120 among 4 February and March, in a men, so that the shares shall common year? be to one another as 1, 2, 3, 4. Ans. 405 cents, or $4 5. cts. Ans. 12, 24, 36, 48. 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 difference Ans. 401280 steps. between half a solid foot and a 21. If a person travel 12mi. solid half foot ? 28rd. in 2 hours, how far does Ans. 648 inches. he go in a minute ? 30. A note was on interest 22. How many lots, each from March 20, 1819, till Jan. eontaining three quarters of 26, 1824 ; what was the length an acre, are there in a square of time? mile ? Ans. 4yr. 10mo. 6d. - Ans. 853 lots, and 40 rods 31. Divide £7 among 8 men -give A. 8d. more than B., 23. If a vintner be desirous and B. 80. 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 32. A horse is valued by A number, how many must he at $60, by B at $69 50, and have ? Ans. 144 of each. by Cat $72 25; what is the 24. There are three fields, average judgment? one containing 7 acres, anoth A. 1 $60 er 10 acres, and the other 12 B. 1 69 50 acres and 1 rood; how many The average in this C. 1 72 25 ease is evidenty shares of 76 rods each are found by dividing the contained in the whole ? 3) 201 75 sum of the several Ans. 61 shares and 44 rods judgments by the Ans. $67 25 number of appraisers. 25. In 172 moidores at 36s. 33. M, N, O, and P appraise each, how many eagles, dol- ed a ship as follows, viz. M at lars and nine-pences, of each $6700, N at $9000,0 at $8750 an equal number? and P at $7380; what is the Ans. 92 of each, and 68 average judgment ? pine-pences over. Ans. $7957 50 over. over. 34. In 5529600 cubic inches, I should pay D $100; and Q how many cords of wood ? said C. should pay D $55; but Ans. 25 eords. R said D should pay C $25; 35. A and B wishing to swap | how was the matter settled ? horses, and disagreeing as to Ans. C pays D $50. the conditions, referred the 37. What is the weight of matter to three disinterested 4hhd. of sugar, each weighing persons, X, Y, and Z, whose 7cwt. 3qrs. 1916. judgments were as follows, viz., Ans. 31 cwt. 2qrs. 20lb. X said A should pay B $8, and 38. Three men and 2 boys Y said A should pay B $6; but hoed 30000 hills of corn, and Z said B should pay A $5; each man hoed two hills while what is the average judgment? a boy hoed one; how many Ans. A must pay B $3. hills were hoed by each man, In the exchange of and how many by each boy? A B articles, where the X1 $$8 judgment of the ref Ans. Each man hoed 7500, Y 1 21 and each boy 3750 hills. 3X2+2-8 Divisor. Ref. 3 5 14 ity, between them, 39. If $911.555 be divided 14 B and partly on other, subtract one among 5 A 5 men and 4 women, side from the other, what is each man and woman's 3)9(3 Ans. and divide the re-share, a man's share being mainder by the num- double that of a woman? ber of referees for the average judg $65.111-wom's share. 36. C and D, wishing to swap farms, referred the subject to 40. Two places differ in lonO, P, Q and R, and agreed to gitude 31° 37' 3''; what is their abide their judgment, which difference in reckoning time, was as follows, viz. said c allowing 15° to make an hour? whould pay D $70; P said C Ans. 2h. 6 281". 5 the Ans. $130.222man's share REVIEW. 1. Whep are number called 7. How is the year commonly di compound, or complex ? vided ? Repeat the number of days 2. By what are the operations in each monih. performed by compound numbers 8. What is meant by leap year! regulated ? How may we know whether a year Repeat the table of Federal is leap year or not? What is meaux money, of English money. by old and new style? What are the names and val- Let the pupil be questioned in file vas of the coins of the United manner respecting the other formen States ? hles. 8. What are the most common 9. What is Reduction 1 Or hon foreign coins 1 what ibeir several many kinds is it? values ? 10. What is the rule for Rection 6. What is the table of time 1 ition Descending? Ascending! 161- 163. PER CENT. 37 11. What is the method of proof 18. If you wish to subtract owe ha each ? date froin another, how would you 12. How would you proceed to proceed ? (152) multiply by 5.1 ? io divide by 5.4 ? 19. What is Compound Multi 13. What is incant by Reduction plication ?-the Rule ? What is of Deciinals ? Compound Division ?-the Rule ! 14. How would you proceed to What relation have these two rules find the value of a decinal in inte- to each other? Of what contrac. gers of a lower denomination ? how. tions are these rules susceptible ? to reduce compound numbers to de- 20. What are the several contraccimals of a biglier denomination ? tions of Simple Multiplication ? (90, 15. How many days are com- 91, 92, 93,)-of Division ? (108, 109, monly reckoned in a month, in com- 110, 111.) pating interest ? (145) 21. What is meant by a simple days and mon!hs reduced to a deci. number? What is the distinction mal of a year ? between a siinple and a compound ? 16. What is Compound Addition ? 22. How would you proceed to ---the Rule?-Proot? take quantities of several denomi17. What is compound Subtrac- nations, each an equal number of tion ?--the Rule !--Proof ? times, from a given quantity ? How are 161. Per Cent. is a contraction of per centum, Latir., signifying by the hundred, and implies that calculations are made by the hundred. Per Annum signifies by the year. Enterest. ANALYSIS. 162. If I lend a neigtibor 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 ? 25 If he pay. 6 cents.--.06 of a dollar (132) for the use of 100 .06 cts. or 1 dollar, he must evidently pay 25 times .06, or (86) .06 times 25=$1.50 for the usc of 25. dollars. Hence, 1.55 23+1.54%26.50 is the suin dve me at the end of the year. 25. Thc $25 is called the principal, the .CG is called the rute per cent., the $1.50 is called the interest, and the $26.50 is 26.50 called the amount. Hence the following DEFINITIONS. 163. Interest is a premium allowed for the use of money. The sum of money upon interest is called the principal. The rate is the per centper annum agreed on, or the interest of one dollar for one year, expressed decimally, 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. SIMPLE INTEREST. 165. Simple Interest is that which is computed on the prinel pal only. FIRST METHOD. ANALYSIS. 166. 1. What is the interest of $38.12 for years, 8 months and 21 days, at 6 per cent. per annum ? Multiplying the principal by, the rate gives the in$38.12 terest for one year, (162) and the interest for one .06 year multiplied by the number of years, is evidently the interest for the whole time. Twenty-one days $2.2872 are pt of a month=0.7, and 8 mo. 21d.38.7 mo. 2.725 But months are 12ths of a year, hence 8.7m. 47 114360 mo.0.725 year (142), and 2yr. 8mo. 21d.2.725 45744 years; we therefore multiply 2.2872, the interest for 160 104 one year, by 2.725, the number of years, and the 45744 producı, $ 6.232, is the interest for the whole time Hence, $6.2326200 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 x has not terminated sooner, has been carried to four places of figures, and that will give the interest sufficiently correct for common practice. When great accuracy is required, find the number of days in the given months and days, and divide ihese by 365, the number of days in a year, and tho quotient will be the true decimal of a year. |