628. Exercises upon the Table. 216. Find D per cent of A.† 217. Find E per cent of A. 218. Find D + E per cent of B. 219. A is D per cent of what sum? 220. A is E per cent of what sum? 221.* B is what per cent of A? 222. Find the commission for collecting or investing A at (D-E) %. 223. If A includes both the commission and sum to be invested, what is the commission at D%? 224. If A includes both the commission and sum to be invested, what is the sum to be invested, the commission being D %? 225. Find the date, which is C years, months, and days after Nov. 27, 1871. 226. Find the interest of $1 at 6% for the time in C. 227. Find the interest of $1 at 1% for the time in C. 228. Find the interest of $1 at D% for the time in C. 229. Find the interest of $1 at E% for the time in C. 230. Find the interest of $1 at (D+E) % for the time in C. 231. Find the interest of A at D% for the time in C. 232. Find the interest of A at (DE) % for the time in C. 233. Find the amount of A at 6% for the time in C. *See note after Exercise 237 234. Find the compound interest of A at D% for 2 y. 9 mo. 18 d. 235. Find the compound interest of A at D% for 1 y. and the months and days in C, interest payable semiannually. 236. Find the amount of A at compound interest for 2 y. 6 mo. 15 d. at 6%. 237. Find the rate, A, B, C being given. (Let the fraction of the per cent be changed to tenths, and the answer be expressed thus: 8.3... .%.) 238. Find the time, A, B, and (D+ E) being given. 239. Find the principal, B, C, D being given. 240. Find the principal, A being the amount, C the time, and 6% the rate. 241. Find the present worth of A, due in the time in C, at D%. 242. Find the discount on A, due in the time in C, at D%. 243. Find the discount on A, due in the time in C, at 6%. 244. Find the bank discount on a note for A, payable in the months and days in C, at D%. 245. Find the avails of a note for A, payable in the months and days in C, at D%. 246. Find the face of a note, which, being discounted at a bank at 6% for the months and days in C, will yield A. + See page 57, for Explanation of the Use of the Drill Tables. 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 g to ? of % to ? 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. e. Read the following expressions: 12:15; $4: $18. 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 consequent is divided, the ratio is multiplied. 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: 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. and; product. 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, S 3:4 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 : NOTE. The ratio of numbers is the same whether the numbers are denominate 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. = 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. |