and how many sheep, if of the number of cows equals of the number of sheep? Ans. Cows, 90; sheep, 80. 109. A farmer has 440 geese and turkeys, and of the number of geese equals of the number of turkeys; how many turkeys must he buy, that of the number of turkeys. may equal of the number of geese? Ans. 88 turkeys. 110. The head of a fish weighs 36 oz., the tail weighs 12 oz. more than the head and of the body, and the body weighs 21 oz. more than the head and tail both; required the weight of the fish. Ans. 259 oz. 111. A company consisting of 50 persons engage a supper at a hotel, but before paying the bill 5 persons withdraw, by which the bill of each was increased 12 cents; what did the supper cost? Ans. $56.25. 112. A steamboat whose rate of sailing was 16 miles an hour sails up a river whose current is 5 miles an hour, and is gone 10 h. 40 min.; how far did the boat go? Ans. 77 mi. 113. A, B, and C eat 63 peaches, of which A owned 40, B owned 23, and C contributed 18 cents; how much of the money ought A and B each to receive, if A eats twice as many as B, and B eats twice as many as C? Ans. A, 8; B, 10. 114. A man having a son in England and a daughter in France, willed if the daughter returned, and not the son, she should have of the fortune, but if the son returned and not the daughter, the widow should have of the fortune; what was the share of each, if both returned and the fortune was $64470? Ans. S., $36840; W., $18420; D., $9210. 115. A drover has 120 sheep in one field, and 2 times as many in another; now, if of the number in each field jumps into the other, what part of the number in the second field equals the number in the first? Ans. 116. A boy bought some apples at the rate of 3 for 1 cent, and as many more at the rate of 5 for 1 cent, and sold them all at the rate of 12 for 3 cents, and thereby lost $4; how many of each kind did he buy? Ans. 12000 of each. 117. of A's age equals of B's, and 10 years is of the difference of their ages; in how many years will of A'ɛ Ans. 12 years. age equal of B's age? 118. A man being asked the time of day, replied that of the time past 8 o'clock A. M., equaled night; what was the time? 119. A had $6435, which equaled of the time to midAns. 6 o'clock P. M. of B's money, minus of their money; of A's, then A and B each paid to C required to know what part of C's equals the sum of A's and B's, if C at first had $47863. Ans. 8. 120. A lady being asked the time of day said, it is between 4 and 5 o'clock, and the hour and minute hands are together; what was the time? Ans. 21 min. past 4. 121. A and B are 650 of B's steps apart, and approach each other; how many steps will each take before they are together, if 3 of A's equal 6 of B's, and A takes 4 while B takes 5? Ans. A, 200; B, 250. as old as her grandas old; how old is each Ans. Mary, 32; Grandmother, 116. 122. Twenty years ago Mary was mother, but 4 years ago she was at present? 123. The sum of two numbers is 212, and of the first, minus 24, is to of the second, plus 24, as to; what are the numbers, and how much must be subtracted from the first that the second may be to the first as to? Ans. { The numbers are 140 and 72; and 59 must be subtracted from the first. 124. Two men engage to build a house for $4800; the first labors as many days as the second, plus 10 days, and receives $2100; how many days does each labor? Ans. 1st, 70; 2d, 90. 125. A lost of his hens; now if he find 50, and sell of what he then has for cost price, he will receive $40; but if he loses 50, and sells of the remainder for cost price, he will receive $20; how many had he at first? Ans. 250. 126. What is the length of a tape that will wind spiralty around a cylinder that is 52 feet long and 3 feet in circumfer ference, provided it passes around the cylinder once every feet? Ans. 65 feet. first? 127. A gave of his money, plus $24 to B, of the remainder, plus $18 to C, of what now remained, plus $12 to C, and then had as much as at first; how much had he at Ans. $180. 128. Having a square yard which contains of an acre, make a gravel walk around it which occupies 1 of the whole yard; what is the width of the walk? Ans. 8 ft. 3 in. 129. A gentleman has a block in the form of a parallelopipedon, which is 48 inches long, 36 inches wide, and 24 inches high; what is the entire surface of the block? Ans. 52 sq. ft. 130. There are 3 balls whose diameters are respectively 3 in., 4 in., and 5 in.; required the diameter of a ball of the same material, weighing as much as the three. Ans. 6 in. 131. A general wishing to draw up his division into a square, found by the first trial he lacked 144 men to complete the square; he then diminished the side of the square by 2 men and had 204 men over; how many men in the division? Ans. 7600. 132. A gentleman has a box whose sides are in the proportion of 2, 3, and 4, which contains 3000 cubic inches; what are the dimensions of the box? Ans. 10; 15; 20. 133. A man sold a horse and carriage for $420; on the horse he lost 20 per cent., and on the carriage he gained 20 per cent.; did he gain or lose, if of the cost of the horse equaled of the cost of the carriage? Ans. Lost $5. 134. A father left his four sons, whose ages were respec tively 5, 9, 13, and 17 years, $27500, to be divided in such a manner that the respective shares being placed out at 5 per cent. simple interest, shall amount to equal sums when they become 21 years of age; what were the shares? Ans. 1st, $5600; 2d, $6300; 3d, $7200; 4th, $8400. 135. If 3 acres of grass, together with what grew on the 3 acres while they were grazing, keep 12 oxen 4 weeks, and in the same manner 5 acres keep 15 oxen 6 weeks; how many oxen can, in the same manner. graze on 6 acres for 8 weeks? Ans. 15 oxen. 18 APPENDIX. THE METRIC SYSTEM OF WEIGHTS AND MEASURES. INTRODUCTION. THE old system of weights and measures in our country is irregular difficult to learn, and inconvenient to apply. The same is true with the old systems of all nations. Originating by chance, rather than by science, they lacked the simplicity of law; and were, therefore, irregular and chaotic. In 1795, France adopted a system of weights and measures called the Metric System, based upon the decimal method of notation, all the divisions and multiples being by 10. It was regarded as so great an improvement upon the old methods that it has since been introduced into Spain, Belgium, Portugal, Switzerland, Holland, Italy, Germany, Austria, Sweden, Denmark, Greece, Mexico, Brazil, and by most of the South American States, and in the most of these countries its use is compulsory. In 1864, the British Parliament passed an act permitting its use throughout the empire whenever parties should agree to use it. The introduction of the Metric System into this country had been long recommended by scientific men, and by such statesman as Madison, Jefferson, John Quincy Adams, etc. In 1866, through the influence of Charles Sumner, Congress authorized its use in the United States, and provided for its introduction into the post-offices for the weighing of letters and papers. To facilitate its adoption, a convenient standard of comparison was furnished, by making the new five-cent piece five grams in weight and one fiftieth of a meter, or two centimeters, in diameter. This system will, without doubt, in a few years be in general use in this country. The advantages of the Metric System are numerous and important. 1. It is easily learned; a school-boy can learn it in a single afternoon. 2. It is easily applied, all the operations being the same as in simple numbers. 3. It does away with addition, subtraction, multiplication, division, and reduction of compound numbers. 4. It will facilitate commerce, giving the nat ons a universal system of weights and measures. 784. The Metric System of weights and measures is based upon the decimal system of notation. 785. In this system we first establish the unit of each measure, and then derive the other denominations by taking decimal multiples and divisions of the unit. 786. Names.-We first name the unit of any measure, and then derive the other denominations by adding prefixes to the unit name. 787. The higher denomination: are expressed by prefix ing to the name of the unit. Deca, Hecto, Kilo, Myria, 10,000 788. The lower denominations are expressed by prefix ing to the name of unit. 789. Units.-The following are the different units, with 790. The Meter is the unit of length. It is the tenmillionth part of the distance from the equator to the poles, and equals 39.37 inches, or 3.28 feet. TABLE. 10 millimeters (mm.) equal 1 centimeter, cm. |