627. DRILL TABLE No. 8. B C D E Time. Per cent. $16.305 1 y. 6 m. 24 d. 5 } $28.14 1 y. 2 m. 6 d. 8 $ 17.083 4 y. 11 m. 3 $ 78.90 3 y. 7 m. 27 d. 2 $100. 2 y. 3 m. 20 d. 7 $50.40 4y. 9 m. 5 d. 4 } $15.08 7 y. 5 m. 18 d. 11 $7.005 2 y. 11 m. 26 d. 1 $430.20 3 y. 10 m. 3 d. 10 $6.095 17 d. 9 $ 30.75 1 y. 3 m. 12 } $175.60 1 y. 4 m. 25 d. 3 $ 290.14 5 y. 21 d. 2 of 1 $ 5.872 1 y. 9 d. 9 1 of 1 $ 25.642 10 m. 13 d. 5 of 1 $11.75 5 y. 7 m. 2 d. 11 of 1 $10.90 2 m. 28 d. 10 } of 1 $3.956 2 y. 8 m. 19 d. 1 of 1 $ 105.20 3 m. 16 d. 4 0.4 $ 5.769 4 y. 8m. 2 d. 8 0.1 $340.50 2 y. 15 d. 7 0.5 $ 75.80 4y. 4 d. $690.40 12 0.07 $500. 4 m. 14 d. 50 0.06 $ 1640. 1d. 100 0.08 $ 64.37 1 y. 7m. 15 d. 7 0.3 $ 654.09 23. 24. 25. $ 10000. 628. Exercises upon the Table. 216. Find D per cent of A. 234. Find the compound interest of 217. Find E per cent of A. A at D% for 2 y. 9 mo. 18 d. 218. Find D+E per cent of B. 235. Find the compound interest of 219. A is D per cent of what sum ? A at D% for 1 y. and the 220. A is E per cent of what sum ? months and days in C, inter221.* B is what per cent of A? est payable semiannually. 222. Find the commission for col 236. Find the amount of A at comlecting or investing A at pound interest for 2 y. 6 mo. (D-E) %. 15 d. at 6% 223. If A includes both the commis 237. Find the rate, A, B, C being sion and sum to be invested, given. what is the commission at (Let the fraction of the per cent D%? be changed to tenths, and the an224. If A includes both the commis swer be expressed thus : 8.3 ... %.) sion and sum to be invested, 238. Find the time, A, B, and (D+E) being given. what is the sum to be invest ed, the commission being D%? 239. Find the principal, B, C, D 225. Find the date, which is C years, being given. months, and days after Nov. 240. Find the principal, A being the 27, 1871. amount, C the time, and 6% the rate. 226. Find the interest of $1 at 6% for the time in C. 241. Find the present worth of A, due in the time in C, at D%. 227. Find the interest of $1 at 1% for the time in C. 242. Find the discount on A, due in the time in C, at D%. 228. Find the interest of $1 at 1% 243. Find the discount on A, due for the time in C. in the time in C, at 6%. 229. Find the interest of $1 at E% 244. Find the bank discount on a for the time in C. note for A, payable in the 230. Find the interest of $1 at months and days in C, at D%. (D+E) % for the time in C. 245. Find the avails of a note for A, 231. Find the interest of A at D% payable in the months and for the time in C. days in C, at D %. 232. Find the interest of A at 246. Find the face of a note, which, (D+E) % for the time in C. being discounted at a bank at 233. Find the amount of A at 6% 6% for the months and days for the time in C. in C, will yield A. * See note after Exercise 237. SECTION XVII. RATIO AND PROPORTION. SIMPLE RATIO. 629. Ten equals how many 2's. Ans. Five 2's. In the above answer we express the relation of 10 to 2 by their quotient. The relation of two numbers expressed by their quotient is ratio. 630. Oral Exercises. a. What is the ratio of 8 to 2 ? of 2 to 8? of 9 to 3? b. What is the ratio of 6 to 2 ? of f to ? off to s ? c. What is the ratio of 5 to 2 ? of 0.5 to 0.2? of 2 lb. to 7 lb.? 631. The ratio of 10 to 2 is indicated thus, 10:2. The expression is read, “The ratio of ten to two." d. Indicate the ratio of 7 to 9; of 8 days to 15 days. 632. The numbers whose ratio is to be found are the terms of the ratio. The two terms of a ratio form a couplet. The first term of a couplet is the antecedent; the second term is the consequent. NOTE. The terms of a ratio must be numbers of the same denomination. 633. As the antecedent of a ratio is the dividend and the consequent the divisor, it follows that When the antecedent is multiplied or the ratio is multiplied. the consequent is divided, When the antecedent is divided or the the ratio is divided. consequent is multiplied, When both terms of a ratio are multi-, the value of the ratio is } plied or divided by the same number, not changed. 634. Examples for the Slate. Find the ratios of the following couplets : (1.) 16 : 256. (4.) 45: 990. (7.) $ 9.00 : $12.50. (2.) 81: 300. (5.) 28 : 910. (8.) $ 0.87} : $ 0.121. (3.) 19:1101. (6.) 64:75. (9.) 100 lb. : 163 lb. 635. The ratio of two numbers is a simple ratio. A simple ratio has one antecedent and one consequent. COMPOUND RATIO. 636. Find the ratio of 2 to 5, and of 3 to 4; and then find the product of these ratios. Ans. f and 4 ; product 2% The product of two or more simple ratios is a compound ratio. 637. The compound ratio given above is indicated thus : 2:51 The expression is read, 3:4 s “The compound ratio of 2 to 5 and 3 to 4.” 638. From Art. 636 it will be seen that when several general numbers form a compound ratio, the value of the ratio may be found by dividing the product of the antecedents by the product of the consequents. 639. Oral Exercises. Find the value of the compound ratios indicated by each of the following expressions : a. 5:8) c. 3: 71 = ? ? 4:9 b. 8:17 d. 7 men : 5 men ? ? 7:45 $ 10.00 : $ 8.00 Å : 12} } NOTE. The ratio of numbers is the same whether the numbers are de. nominate or general ; hence, in finding the value of the ratio in the last example, the terms may be regarded as general numbers. PROPORTION. 640. What is the ratio of 3 ft. to 6 ft.?. of $ 5 to $10 ? These ratios are equal to each other. An equality of ratios is a proportion. 641. The equality of the above-named ratios is expressed thus, 3 ft. : 6 ft. = $5:$ 10. This expression is read, “ 3 ft. is to 6 ft. as $5 is to $10." 642. Exercises. Read the following: a. 5:7 = 15 : 21. c. 40 : 10 = 15 min. : 37 min. b. }:3= $7: $105. d. 9:6=6: 4. 643. The first and fourth terms of a proportion are the extremes, and the second and third are the means. Note I. In Example d above, 6 is the consequent of the first couplet and the antecedent of the second ; and so 6 is a mean proportional between 9 and 4. Note II. Four quantities are directly proportional when the first is to the second as the third is to the fourth. Four quantities are inversely proportional when the first is to the second as the fourth is to the third ; or when one ratio is direct and the other inverse. Thus, the amount of work done in any given time is directly proportional to the number of men employed; that is, the more men, the more work: but the time occupied in doing a certain work is inversely proportional to the number of men employed; that is, the more men, the less time. To supply a Missing Term of a Proportion. 644. ILLUSTRATIVE EXAMPLE. Supply the missing term denoted by x in the proportion, x: 5=4:10. Explanation. - The ratios of the two coupX : 5=4:10 lets are in and 1; these changed to fractions having a common denominator are *X10 and WRITTEN WORK. 5x10 As these fractions are equal, and their denominators the same, their numerators must be equal. But one numerator is the product of the means of the proportion, and the other 10 2:5=4:10 |