242. The product of three factors is 191; two of the factors are 51 and 11; what is the third factor ? Ans. 23. 243. How much gold will $500 currency buy, when gold is worth $1.25 ? Ans. $400. 244. If 12 men in 5 days of 8 hours plough 60 acres of land, how many men will plough 100 acres in 8 days of 10 hours each? Ans. 10 men. 245. What is the bank discount of $600 for 3 months at 7%? Ans. $10.85. 246. What is the amount of $600 at 6% compound interest, for 10 years, payable annually ? Payable semiannually? Ans. Annually, $1074.51; semi-annually, $1083.67. 247. What principal at 6% will amount to $960 in 2 yr. 6 mo., simple interest? Ans. 960 x 148 = $834.78 11% 248. A man owning of a bank, sold 30% of his share; what per cent of the whole had he left ? Ans. 46% 249. Add 100.01, 1000.001, 10000.0001, 12.004, 10.0004, 9.00003. Ans. 11131.01553. 250. The means of a proportion and one extreme; thus, 3:4 :: 9:?. Ans. 12. 251. The extremes and mean given; thus, 2:6 :: ?:9. Ans. 3. 252. One couplet of a ratio and one term of another, to find the second term; thus, and 6 ? Ans. 15. one COR. 1.-When the two means and one extreme are given, divide the product of the means by the given extreme. 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 용 at %; 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, $14854. 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. 3% 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. a 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". 264. 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 proportional to the other two terms. 266. What is the value of a fraction multiplied by its denominator ? Ans. The numerator becomes an integral number. a 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. indicate ? Ans. 30° 268. If Fahrenheit is at 770, what will R. indicate ? Ans. 20°. NOTE.-212 — 32 = 180; the ratios will be formed by the num. bers 180, 100, 80, and will be C = F, R = F, C = IR, R = AC, F = ? C, and F 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. 3995611f 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 = ti ; 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. 69.15+ miles. a 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 127% of C's; B has $50 more than C; how much has each ? Ans. A has $25, B $250, and C 8200. 277. If a globe of gold 4 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 money? Ans. 4s. 11d.+: NOTE.—24 carats gold is pure gold ; 18 carats has 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. 3lb. 281. 140 is 20% less than what ? Ans. 175. 282. 168 is 20% more than what ? Ans. 140. 283. 5-10 is 331% 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 ? Ans. 1296 bushels. |