$462.75. Baltimore, Aug. 1, 1848. Ninety days from date, for value received, we promise to pay Marcus Willis, or order, four hundred and sixty-two 70 dollars. JACKSON & ELLIS. 377-391. What would be received for each of the above notes, if discounted at 5 per cent.? at 7 per cent.? at 8 per cent.? 392. What is the value of a note at 30 days for $8750, discounting at 5 per cent.? 393. What is the value of a note at 60 days, for $1200, discounting at 4 per cent.? 394. What is the value of a note at 90 days for $975, discounting at 47 per cent.? 395. What is the value of of of a note at 120 days, for $2000, discounting at 5 per cent.? 396. What is the value of a note at 90 days for £63 17s. 6d., discounting at 4 per cent.? 397. What is the difference between the equitable discount, (§ 126,) and the bank discount, on $487.50, for 63 days? 398. How much would be gained by purchasing molasses for $1600 cash, and selling it immediately for $2000, payable in 4 months-the Mechanics' Bank discounting the note at 5 per cent.? 399. What is the value of a note at 60 days, for the amount of the following bill? 163gyd of silk, at 87 cts. a yd.; 127 yd. India muslin, at 621⁄2ct. a yd.; 97‡' yd. Alpacca, at 93 ct. a yd.; 225yd. merino, at 50ct, a yd.; and 115ğyd. printed lawn, at 37 ct. a yd. 400. Lowell, July 17, 1848. 64cwt. of sugar at 5 ct. a pound. at $4.621. a barrel. at 8gct. a pound. 2cwt. 1qr. 17lb. of rice, at $3.50 a cwt. 13 boxes candles, each 324lb. at 29 ct. a pound. Received payment by note at 90 days. WILLIAM SIMPSON & Co. How much would be received on the note, if dis counted at 7 per cent.? QUESTIONS ON CHAPTERS VI., VII., VIII., AND IX. What is a PRIME NUMBER? a composite number? Name all the prime numbers less than 100. How can you tell whether any number can be divided by 2, 5, 3, 9? How do you find the prime factors of any number? How do you determine whether any number is a prime? What is meant by a multiple? a common multiple the least common multiple? How do we find the least common multiple of two or more numbers? Show that this pro cess will give the least common multiple. What is a common divisor? the greatest common divisor? How do we find the greatest common divisor? Why do we proceed in this manner? What is cancelling? How do you cancel? When you have cancelled all the numbers in either the dividend or divisor, what must be put in their place? When the divisor is a composite number, how may we obtain the quotient? What are FRACTIONS? In how many different ways may they be read? Show why each of these ways may be adopted. What is meant by the numerator? the denominator? the terms of a fraction? What is shown by the numerator? by the denominator? How is the value of a fraction affected by increasing the denominator? the numerator? by diminishing the numerator? the denominator? What is a mixed number? How would you find what part 324 is of 187? Why? What is REDUCTION? How do we reduce fractions to whole numbers? to mixed numbers? to decimals? Explain these reductions. What are proper fractions? improper fractions? When is a fraction greater than 1? less than 1 equal to one? How would you write a decimal in the form of a fraction? Explain the rule for reducing whole or mixed numbers, or decimals, to fractions. Explain the method of reducing compound to simple fractions; fractions to their lowest terms; fractions to a common denominator; complex to simple fractions; fractions to others having any given numerator or denominator. Explain the rules for addition, subtraction, multiplication and division of fractions. What are INFINITE DECIMALS? What is the repetend? How is it distinguished? To what is every repetend equivalent? Show that it is so. How then would you reduce any infinite decimal to a fraction? How may addition and subtraction of infinite decimals, be performed without reducing them to fractions? What are COMPOUND NUMBERS? Repeat the table of Federal Money; English Money; Troy Weight; Apothecaries' Weight; Avoirdupois Weight; Long Measure; Cloth Measure; Square Measure; Cubic Measure; Dry Measure; Liquid Measure; Circular Measure; Time Measure. How many shillings in a guinea? How many dollars in a pound sterling? How do we find the area of a rectangular surface? How many cubic feet make a foot of wood, or a cord foot? How many cord feet in a cord? How many cubic feet in a ton of round timber? a ton of square timber? a ton of shipping or storage? How do we find the solid contents of any rectangular solid? For what purpose are each of the weights and measures used? How many cubic inches in a half peck? in a common gallon? in a gallon of milk or of malt liquor? For what purpose is the hogshead (measure) used? How many degrees in a quadrant? in a sign of the zodiac? How many days in a leap year? What years are leap years? Repeat the number of days in each month. In mercantile business how many days are considered as making a month? In Chap. VIII., § 109, solve examples 821, 816, 810, 830, 807, 806, 779, 780, 772, 784, and give your reasons for each step. Give, in your own language, a rule for reducing higher denominations to lower; lower denominations to higher; for compound addition; compound subtraction; compound multiplication; compound division. Explain each rule. Can fractions and decimals be reduced by the same rule as whole numbers? What is meant by PER CENT.? How do we compute any required percentage? Why? What is meant by commission? insurance? premium? policy? underwriters? taxes? stocks? the par value? the dividend on a stock? When is a stock said to be above par? below par? at a discount? at an advance? What part of the original cost is stock worth, that sells at 164 per cent. below par? at 12 per cent. advance? at a discount of 173 per cent.? at 25 per cent. above par? What is meant by duties? specific duties? ad valorem duties? draft? tare? gross weight? net weight? In custom house business, what allowance is made for leakage and breakage? for draft? How do we find what per cent. is gained or lost by any transaction? What is INTEREST? simple interest? compound interest? What is the principal? the rate? the amount? Give, in your own language, the General Rule for Interest? the Bank and Business Rule? Show how each rule is obtained. What is a promissory note? an endorsement? What is the usual mode of computing interest on notes that are settled within a year from their date? What is the Legal Rule? How do we find the amount of any sum at compound interest? How do we find the compound interest? How do you find the rate, when the principal, interest, and time * The number of square feet, rods, or acres, &c., in any surface, is called its area. are given? the time, when the principal, interest, and rate are given? the principal, when the time, rate, and interest are given? the principal, when the time, rate, and amount are given? Explain the reasons for each of these methods. What is DISCOUNT? equitable discount? bank discount? How do you find equitable discount? bank discount? What are days of grace? How many days of grace are usually allowed? X. ANALYSIS AND RATIO. 128. ANALYSIS is the examination of any proposed question, to determine the proper method for its solution. In every question, one or more things are given, (which are sometimes called the known quantities,) and one or more things are required. The required quantities are often called unknown quantities. If the value of ONE of each of the unknown quantities can be found, the value of ANY number of them can be readily determined, (§ 35.) Therefore, whenever there is any difficulty in solving a question, we should first endeavor to find the value of ONE of each unknown quantity. In most cases, this can be easily done by the method stated in § 55. The following may be given as the GENERAL RULE FOR ANALYSIS. First endeavor to find the value of ONE of each unknown quantity, and then by multiplication, find the value of the REQUIRED NUMBER. In every question, EXPRESS the operations that are to be performed, (as far as it is possible to do so,) and shorten your work by CANCELLING, whenever you can. EXAMPLE. If 10 men can build a wall in 6 days, în what time could it be built by 15 men? The question is, " in how many days would 15 men build the wall?" and we first find in how many days ONE man would build it. It would take 1 man 10 times as long as 10 men, or 10 x 6 days. It would take 15 men only as long as 1 man, or of 10 x 6 days, or' 129. EXAMPLES FOR THE PUPIL. 1-10. How long would it take 9 men to consume a stock of provisions, that would last 15 men 18 weeks? How long would it take 10 men? 6 men? 5 men? 30 men? 27 men? 45 men? 54 men? 90 men? 135 men? 11-20. If a stock of provisions is sufficient to supply 36 men for 35 weeks, how many men would consume it in 6 weeks? in 7 weeks? 30 weeks? 14 weeks? 15 weeks? 21 weeks? 10 weeks? 28 weeks? 42 weeks? 63 weeks? 21-30. If 15 men consume 70 pounds of provisions in a day, how many men would consume 112lb. in the same time? How many would consume 42lb.? 140lb.? 28lb. 84lb.? 126lb.? 56lb.? 98lb.? 840lb.? 196lb. ? 31-40. If 19 yards of broadcloth cost $85.50, what will be the cost of 13yd.? 27yd.? 84yd.? 53yd.? 491yd.? 6.875yd.? 99yd.? 374yd.? 3 yd.? tyd.? 41-50. How long will it take 13 men to eat a stock of provisions, that 9 men can eat in 26 days? How long will it take 6 men? 18 men? 26 men? 39 men? 36 men? 24 men? 54 men? 78 men? 117 men? 51-60. If it takes 3 yards of cloth that is 4 quarters wide, to make a coat, how many yards would it take of cloth 3 quarters wide? 2 quarters? 6qr.? 5qr.? 8qr. 44qr.? 15qr.? 33qr.? 51qr.? 44qr.? 61-70. If 94yd. of cloth that is 6qr. wide will make a cloak, how many yards would be required, that is 54qr. wide? 7qr. wide? 8qr. wide? 4qr. wide? 61qr. wide? 7qr. wide? 34qr. wide? 43qr. wide? 9qr. wide? 7qr. wide? 71-80. If 4 acres of land cost $28.12, what is the price of 3 acres? 7 acres? 51A.? 64A.? 118A. ? 19A.? 95A.? 17A.? 8.25A.? +§A.? |