then uses 15 loads and finds that the quantity left, is to the quantity sold, as 1 to 2. Required the number of loads at first in the stack. 227. There are two 3 times the less, and the the sum of the numbers. numbers, the greater of which is sum of their squares is 8 times What are they? 228. Find two numbers in the proportion of 4 to 7, the square of whose product is 63504. 229. A farm of 750 acres is divided among three persons. B. has as much as A. and C. wanting 10 acres, and the shares of A. and C. are to each other in the proportion of 7 to 3. Required the share of each. 230. If 11 oxen eat 244 acres of grass in 5 weeks, and 10 oxen eat 19 acres in 4 weeks, how many acres of similar pasture will 42 oxen eat in 7 weeks, the grass growing uniformly? 231. What number is that which is 169 greater than the greatest square number below, and 114 less than the least square number above itself? 232. A. and B. can do of a piece of work in a day, B. and C. can do of it in 24 days, and A. and C. can do of it in 41 days. In what time would each do it alone, and in what time would it be done if they all worked together? 233. Find the least 3 integers, such that of the first, 15 of the second, and of the third, shall be equal. 20 234. An estate of $20000 is to be divided among three sons, two daughters, and a widow; each son is to receive 3 times as much as a daughter, and each daughter twice as much as the widow. Required the share of each. 109 235. An usurer left his fortune to be disposed of in the following manner: To A. , to B. 3 to C., to D., to E. o, to F. and the remainder, which was $800, was to be paid to C. the share of each? 509 What was the whole estate, and what was 236. For the lease of a certain estate, A offers $150 premium, and $300 rent per annum; B. offers $400 premium, and $250 per annum; C. offers $650 premium, and $200 per annum; and D. offers $1800 in ready money. Whose offer is the best, and what is the difference between them, computing 5 per cent, compound interest? 237. Which is of the greater value, the income of an estate of $500 a year for 15 years to come, or the reversion of the same estate for ever, at the expiration of the 15 years, interest at 6 per cent.? 238. If a ball were put in motion by a force which would drive it 12 miles the first hour, 10 miles the second, and so on in geometrical progression, what distance would it go in the whole? 239. What is the least number, which, if divided by 2, will leave 1 remainder, by 3 will leave 2, by 4 will leave 3, by 5 will leave 4, by 6 will leave 5, but by 7, will leave no remainder? 240. Required the least three numbers, which, divided by 20, will leave 19 remainder, if divided by 19 will leave 18, and so on, (always leaving one less than the divisor,) to unity. 241. A trader offers to receive a young man as partner, proposing, if he will advance $500, to allow him $200 per annum; if he will advance $1000, to allow $275 per annum ; and if he advance $1500, he will allow $350 per annum. What per cent. is offered for the use of the money, and how much for the young man's time? 242. Arnold's stock in the firm of Arnold and Benton, exceeded Benton's by $2000; Arnold's money continued in trade 5 months, and Benton's 9 months. Required each man's investment, the gain being equally divided. 243. A shepherd sold to one man half his flock and half a sheep, to a second half the remainder and half a sheep, and to a third half the remainder and half a sheep, when he had 20 left. How many had he at first? END OF PART SECOND. USE OF THE TABLES. I. PRIME AND COMPOSITE NUMBERS. The hundreds are placed at the head of the table, and the tens and units at the left hand. Then, if it be desired to find 5609, look for 56 at the top, and 09 at the side, and at the angle of meeting we find 71, which is one of the factors. Dividing by 71 we obtain 79, which being a prime number is the only remaining factor. For numbers below 1000, all the factors are given. For all odd numbers above 1000, one or more factors will be found in the table, which will reduce the number to a prime or to some composite number less than 1000, when the remaining factors can be found. Primes are indicated by a dash (-). The index written against any number, indicates the number of times it is employed as a factor. Thus, 32 = 3 × 3; 53 = 5 × 5 × 5. II. COMPOUND INTEREST. The amount of any principal, is found by multiplying the principal by the amount of $1.00 for the time. If the time consists of years, months, and days, the amount for the given number of years, must be multiplied by the amount of $1.00 for the remaining months and days. The present worth at compound interest, of any sum due at a future time, is found by dividing the given sum by the amount of $1.00 for the time. III. THE AMOUNT OF ANNUITIES. To find the amount of any annuity; multiply the given annuity by the amount of an annuity of $1.00 for the time. If the annuity is payable semi-annually, take the amount for twice the time, at half the rate. IV. PRESENT WORTH OF ANNUITIES. Multiply the given annuity by the present worth of an annuity of $1.00 for the given time. The present worth being given, to find the annuity; divide the present worth by the present worth of an annuity of $1.00 for the same time. |