sell the house for exactly what it cost, with reference to interest on the money expended, and take the purchaser's note for the amount, what shall be the face of the note, and what its date? 6. THOMAS WHITING, 1859. Face, $2007.75. Ans. Date, March 8, 1856. TO ISRAEL PALMER, Dr. .$420 135 ..1800 Jan. 1. To 60 bbls. Flour, @ $7.00... 66 66 If credit of 3 months be given to each item, when will the above account become due ? Ans. May 30. CASE III. 363. When the terms of credit begin at different times, and the account has both a debt and a credit side. 1. Average the following account: 35450 ÷ 600 = 59 da., average term of interest. ANALYSIS. In the above operation we have written the dates, showing when the items become due on either side of the account, adding 3 days' grace to the time allowed to the draft. The latest date, Oct. 20, is assumed as the focal date for both sides, and the two columns marked da. show the difference in days between each date and the focal date. The products are obtained as in the last case, and a balance is struck between the items charged and the products. These balances, being on the Dr. side, show that David Ware, on the day of the focal date, Oct. 20, owes $600 with interest on $35450 for 1 day. By division, this interest is found to be equal to the interest on $600 for 59 days. The balance, $600, therefore, has been due 59 days. Reckoning back from Oct. 20, we find the date when the balance fell due, Aug. 22. RULE. I. Find the time when each item of the account is due; and write the dates, in two columns, on the sides of the account to which they respectively belong. II. Use either the earliest or the latest of these dates as the focal date for both sides, and find the products as in the last case. III. Divide the balance of the products by the balance of the account; the quotient will be the interval of time, which must be reckoned from the focal date TOWARD the other dates when both balances are on the same side of the account, but FROM the other dates when the balances are on opposite sides of the account. 2. What is the balance of the following account, and when is it due? JOHN WILSON. Dr. Cr. 1859. 1859. 66 To Mdse. 448 00 Jan. 20 By Am't bro't forward 560 00 1 Carriage. "Cash.... 264 00 990 00 3. If the following account be settled by giving a note, what shall be the face of the note, and what its date? Give analysis. Rule. 364. Ratio is the comparison with each other of two numbers of the same kind. It is of two kinds-arithmetical and geometrical. 365. Arithmetical Ratio is the difference of the two numbers. 366. Geometrical Ratio is the quotient of one number divided by the other. 367. When we use the word ratio alone, it implies gcometrical ratio, and is expressed by the quotient arising from dividing one number by the other. Thus, the ratio of 4 to 8 is 2, of 10 to 5 is, etc. 368. Ratio is indicated in two ways. 1st. By placing two points between the numbers compared, writing the divisor before and the dividend after the points. Thus, the ratio of 5 to 7 is written 5:7; the ratio of 9 to 4 is written 9: 4. 2d. In the form of a fraction; thus, the ratio of 9 to 3 is; the ratio of 4 to 6 is . 369. The Terms are the two numbers compared. 370. The Antecedent is the first term. 371. The Consequent is the second term. 372. No comparison of two numbers can be fully explained but by instituting another comparison; thus, the It is thought best to omit the questions at the bottom of the pages in the remain. ing part of this work, leaving the teacher to use such as may be deemed appropriato. comparison or relation of 4 to 8 cannot be fully expressed by 2, nor of 8 to 4 by . If the question were asked, what relation 4 bears to 8, or 8 to 4, in respect.to magnitude, the answer 2, or, would not be complete nor correct. But if we make unity the standard of comparison, and use it as one of the terms in illustrating the relation of the two numbers, and say that the ratio or relation of 4 to 8 is the same as 1 to 2, or the ratio of 8 to 4 is the same as 1 to 1, unity in both cases being the standard of comparison, then the whole meaning is conveyed. 373. A Direct Ratio arises from dividing the consequent by the antecedent. 374. An Inverse or Reciprocal Ratio is obtained by dividing the antecedent by the consequent. Thus, the direct ratio of 5 to 15 is 15 = 3; and the inverse ratio of 5 to 15 is. 375. A Simple Ratio consists of a single couplet; as 3:12. 376. A Compound Ratio is the product of two or more simple ratios. Thus, the compound ratio formed from the simple ratios of 3: 6 and 8: 2 is § × 3 × 8:6 × 2 = }=}. = 377. In comparing numbers with each other, they must be of the same kind, and of the same denomination. 378. The ratio of two fractions is obtained by dividing the second by the first; or by reducing them to a common denominator, when they are to each other as their numerators. Thus, the ratio ofis÷= }} = 2, which is the same as the ratio of the numerator 3 to the numerator 6 of the equivalent fractions and. Since the antecedent is a divisor and the consequent a dividend, any change in either or both terms will be governed by the general principles of division, (87.) We have only to substitute the terms antecedent, consequent, and ratio, for divisor, dividend, and quotient, and these principles become GENERAL PRINCIPLES OF RATIO. PRIN. I. Multiplying the consequent multiplies the ratio; dividing the consequent divides the ratio. PRIN. II. Multiplying the antecedent divides the ratio; dividing the antecedent multiplies the ratio. PRIN. III. Multiplying or dividing both antecedent and consequent by the same number does not alter the ratio. These three principles may be embraced in one GENERAL Law. A change in the CONSEQUENT produces a LIKE change in the ratio; but a change in the ANTECEDENT produces an OPIOSITE change in the ratio. 379. Since the ratio of two numbers is equal to the consequent divided by the antecedent, it follows, that 1. The antecedent is equal to the consequent divided by the ratio; and that, 2. The consequent is equal to the antecedent multiplied by the ratio. EXAMPLES FOR PRACTICE. 1. What part of 9 is 3? = ; or, 9:3 as 1:1, that is, 9 has the same ratio to 3 12. What is the ratio of 3 gal. to 2 qt. 1 pt? Ans. • |