COR. 2.- When the two extremes and one mean are given, divide the product of the extremes by the given mean. COR. 3.—When one couplet, forming a ratio, is given, and one term of another couplet, to form an equal ratio : The ratio of the unknown to the similar term must be the same as.of the given similar terms. 253. A house valued at $6000 is insured for its value at 3%; what is the premium ? Ans. $30. 254. A clerk at a salary of $1000, pays $250 for board, $175 for clothing, and $225 for other expenses ; what per cent of his salary is left ? Ans. 35% 255. Two merchants engage in business; the one puts in $8000 and the other $6000; the latter is to receive $500 extra annually for his attention to the business; if the gain is $2800 annually, what is each one's share ? Ans. First, $1314%; and second, $1485%. 256. Bought 200 lb, bacon at 8 ct. per lb., and when I sold it at 10 ct. per lb. I found it had lost in weight $; did I gain or lose and how much ? Ans. Gained $1.50. 257. What will it cost to enclose in one square field 160 acres of land, the fence costing $1.50 per rod ? Ans. $960. 258. The premium for the insurance of property for $12000 was $90; what was the rate per cent? Ans. %. 259.'A man has 50% of his property invested in a farm, 10% in a house, 15% in stock and farming implements, and the balance $3000 in bank; what is the amount of his property ? Ans. $12000. 260. If 40 acres of land form a square, what is the length of a side? Ans. 80 rods. 261. If 80 acres are in the form of a rectangle, the length being double the width, what are the dimensions ? Ans. Length 160 rods, breadth 80 rods. 262. Bought a carriage for $258.75, which was sold at a profit of 15%; what was the original cost? Ans. $225. 263. The difference in the time of St. Petersburg and Washington is 7 hr. 9 min. 19 sec. ; what is the difference in longitude ? Ans. 107° 19' 45". 204. In what terms of a proportion may equal factors be cancelled without altering the ratios? Ans. In both terms of the same couplet, in both antecedents, or in both consequents. 265. How is a proportion formed with only three numbers ? Ans. By repeating the middle number; thus, as 2:4 :: 4:8; and the 4 is said to be a mean propor 3 tional to the other two terms. 266. What is the value of a fraction multiplied by its denominator ? Ans. The numerator becomes an integral number. REM.-In Fahrenheit's thermometer, the freezing point of water is 32° and the boiling point 212°; in the Centigrade, the freezing point is 0° and the boiling 100° ; in Raumer's, the freezing is 0° and the boiling 80°. 267. If Fahrenheit is at 86°, what will C. indicatė ? Ans. 30°. 268. If Fahrenheit is at 770, what will R. indicate ? Ans. 209. = NOTE.—212 — 32 = 180; the ratios will be formed by the num. bers 180, 100, 80, and will be C = F, R = f F, C = R, R C, F = ? C, and F = R. REM.—Two bodies attract each other inversely as to their weights. 269. Suppose the earth and moon were not interrupted by any other attractions, their weights being as 49147 and 123 respectively; how many miles would the moon move whilst the earth moved 100 miles ? Ans. 3995611 miles. 270. At what time between 3 and 4 o'clock are the hour and minute hands together? Ans. 3 hr. 16,4 min. REM.-Whilst the hour hand goes the space of 5 minutes, the minute hand goes the round of the dial 60 minute spaces; the gain is t = t; that is, in 1 hour it gains 55 minutes, or it gains 11 in 12. At 3 o'clock the hands are 15 minute spaces apart, and this is to be gained until they are together; therefore, as 11 gain : 3 gain :: 12 hr. : 3 hr. 161 min. 271. At what time between 4 and 5 is the minute hand 5 minute spaces behind the hour hand ? Ans. 4 hr. 164 min. REM.-The gain is the same as in 270. 272. At what time between 4 and 5 is the minute hand 5 minute spaces ahead of the hour hand ? Ans. 4 hr. 27 min. 273. The diameter of the earth is 7924 miles ; what is its circumference ? Ans. 24894.0384. 274. What is the length of a degree of a great circle ? Ans. 09.15+ miles. 275. The diameter of the Arctic and Antarctic Circles is 2625.5 miles; what is the length of a degree of longitude there? Ans. 22.9+ miles. REM.-At the poles all the degrees of longitude come to a point. 276. A's money is 10% of B's, and 12% of C's; B has $50 more than C; how much has each ? Ans. A has $25, B $250, and C $200. 277. If a globe of gold | in. in diameter is worth $15, what is the value of a globe 4 in. in diameter? Ans. $61440. 278. How far distant is a cloud in which lightning is seen 15 seconds before the thunder is heard ? Ans. 16500 feet. NOTE.-Sound moves 1100 feet and light 192500 miles in a second. 279. What is the value of one dollar U. S. in English Ans. 4s. 14d.+ NOTE.—24 carats gold is pure gold ; 18 carats bas 6 carats alloy, 16 carats has 8 carats alloy, etc.; the alloy is generally copper and silver. 280. A refiner melts 8 lb. gold 20 carats fine with 12 lb. 22 carats fine; how much alloy must be added in order to make it 18 carats fine ? Ans. 38 lb. 281. 140 is 20% less than what ? Ans. 175. 282. 168 is 20% more than what ? Ans. 140. 283. 510 is 333% more than what? Ans. 405. 284. A lost $5, which was 25% of what he had left; how much had he at first ? Ans. $25. 285. Sold 324 bushels of wheat, which was 331% of what I had left; how many bushels in the whole crop? Áns. 1296 bushels. money? 286. If 20% of 37% of 331% of a number is 4, what is the number? Ans. 160. 287. If the cost of a coat is $30, the trimmings cost 60% less, and the making 40% less than the cloth, what did each cost ? Ans. Cloth $15, trimming $6, making $9. 288. If I sell ş of an article for what the whole.cost, what per cent do I gain? Ans. 50%. 289. If I sell of an article for what cost, what per 를 cent do I gain ? Ans. 113%. 290. What is the cost of grading 2 miles of railroad, averaging 3 feet in depth or height, and 12 feet wide, at 30 cents per cubic yard ? Ans. $4224. 291. I sold goods through a broker who charged me 27%; my commission was 43%; the transaction netted me $50; for what were the goods sold ? Ans, $2000. ); 292. A hare is 75 leaps ahead of a hound, and the hare takes 2 leaps while the hound takes one, but two of the hound's leaps is equal to five of the hare; how many leaps must the hound take to overtake the hare ? Ans. 150 leaps. NOTE.—Whilst the hound takes two leaps the hare takes four leaps, but the two leaps of the hound is equal to five of the hare; hence the hound gains 1 hare leap on the hare for every two leaps the hound takes. 293. A tank is 24 ft. long, 8 ft. wide, and 9 ft. high ; how many bushels of wheat will it hold ? Ans. 1388} + bu. 294. How much currency at 121% discount, will purchase 50 shares ($100 each) of bank stock at a premium of 12%? Ans. $6400. |