multiplied by the difference between 31 and 2, and the product to be taken 99. How many are 3 + §−(3+ 1) × (3} — 2})? -- Ans. 12 100. (++8 − 3 + } + { ) × 54 ? 103.÷(2+)–÷12=? 104. of 8=? 71 54 = -- 13 Ans. 117. 105. £s. + fd. — ‡ qr. = what fraction of a pound? 106. 273 is a divisor, and 5 is the quotient; what is the 107. The sum of two numbers is 87, and one of the numbers 108. The difference of two numbers is 173, and the less num- 109. 48 is a dividend, and 24% is the quotient; what is the 110. 47% is the product of two factors, and 123 is one of those 111. A farmer, owning 144 acres of land, cultivated 2 acres 112. The distance from the earth to the sun is about 95000000 miles ; in what time will a car run that distance, running 37 miles per hour, allowing 365 days in a year? Ans. 288y. 363d. 13h. 20m. 113. A purchased 221b. sugar at 64 cents, 10lb. tea at of a dollar, 50lb. rice at 4 cents, 1bbl. flour at $63, and 38 yardı of sheeting, and gave 2 ten-dollar bills to the merchant, who returned $33; required the price per yard of the sheeting? 114. If the cargo of ship be worth $72000; and if of of of the cargo be worth of 3 of 14 of the ship, what is the value of the ship? Ans. $24000. 115. The cargo of a certain ship is worth $48000, and if § of the value of the cargo is the value of the ship; what is the value of the ship? Ans. $12000. feet in length, 15 feet in width, room are 4 windows, each 3 feet 116. A certain room is 16 and 83 feet in hight. In this wide by 4 feet high, having 12 panes in each window; also, 4 doors, each 3 feet wide by 8 feet high; the base-boards are of a foot wide. A glazier furnishes and sets the glass for 15} cents per pane, a painter paints the doors, base, and floor for 31 cents per square foot, and a mason plasters the room for 22 cents per square yard. What is the cost of glazing, painting, and plastering? Ans. $34.94§. 117. If 9£ sterling money equals 12£ N. E. currency, 6£ N. E. equals 8£ N. Y., 16£ N. Y. equals 15£ N. J. and 45£ N. J. equals 28£ Ga. currency, how many pounds sterling are equal in value to 56£ Ga: currency? Ans. 54. 118. A man hired a laborer for 50 days, on condition that for every day he worked he should receive $1.50 and for every day he was absent he should forfeit $1.75. At the expiration of the time he received $42.50. How many days was he absent? 119. A teacher, being asked how many scholars he had, replied, if I had as many more, and as many more, and 361 scholars, I should have 300; how many had he? Ans. 93. 120. A gentleman being asked the time, replied that of the time past from noon was equal to of the time to midnight; what was the time? 121. The radii of two circles having a common center are 4 and 8 inches; what is the area of the circular ring included between the two circumferences? Ans. 150.796416sq. in. REMARK. The answer to Ex. 121 may be found without ascertaining the area of either circle. How? 122. Hiero, King of Syracuse, ordered his jeweler to make him a crown of gold, weighing 63 ounces. The artist attempted a fraud by substituting a portion of silver; but the king suspecting fraud, requested Archimedes to examine it. Archimedes putting it into water, found that it displaced 8.2245 cubic inches of water; and having found that an inch of gold weighs 10.36 ounces, and an inch of silver 5.85 ounces, he discovered what part of the king's gold had been purloined. It is required to repeat the process. Ans. 28.80355+ ounces. 123. A tree 32 feet tall, growing vertically upon a horizontal plane, is broken off so that the top reaches the ground 16 feet from the stub, the part broken off turning upon the top of the stub as upon a hinge; what is the hight of the stub? Ans. 12 feet. 124. A drover bought a number of horses, oxen, and cows for $2640. For every horse he paid $50, for each ox § as much as for a horse, and for each cow as much as for a horse. There were 3 times as many oxen as horses, and twice as many cows as oxen. How many were there of each? 125. Received a quantity of goods from Liverpool, with instructions to sell them and invest the proceeds in cotton, after deducting a commission of 1 per cent. on the sales of the goods and 1 per cent. on the purchase of the cotton. Sold the goods at an advance of 5 per cent. on the invoice price, and received $12600; what was the invoice price, and what sum was invested in cotton? Ans. Invoice, $12000; invested, $12288.11. 126. A, B, and C do a piece of work; A and B together do of it, and B and C together do of it; what part does each do? 127. A can perform a piece of work in 6 days of 10 hours each, and B can do the same in 8 days of 11 hours; in how many days of 11 hours can A and B together do the work? 128. Divide $15500 among 3 officers and 8 sailors so that each officer shall receive 2 times as much as each sailor. 129. A man gave of his estate to A, 7 of the remainder to B, and the rest to C. A received 257£ 3s. 4d. more than B; what did C receive? 130. A owns of a field, and B the remainder; the difference between their shares is 7a. 3r. 15дrd. What is B's share? 131. The angle formed by the perpendicular and hypothenuse of a right-angled triangle is 30° and the square of the perpendic ular is 75; what is the base? 132. A watch has an hour, a minute, and a second hand, turning upon the same center-staff. At 12 o'clock the three hands are together. How long will it be (1) before the second-hand will be equally distant from the other two? (2) before the minute. hand will be equidistant from the other two? (3) before the hour-hand will be equidistant from the other two? Hence the proportion: As the distance round the clock is to the distance the hour-hand has moved, so is the number of seconds while the hour-hand is going round the clock to the number of seconds required; i. e., As 1427 1: 43200sec.: 30sec., Ans. REMARK. In a similar manner we may determine when the second-hand shall be at s' represented in Fig. 1 and all similar examples may be solved in like manner. 133. At what time between 12 and 1 o'clock will the hour and minute hands of a watch make equal acute angles with the line extending from the center-staff to 12? Ans. 55m. past 12. 9 10 Fig. 2. 12 11 ii/ h/h1 TH 2 ANALYSIS. At half-past 12 the minute-hand is at 6 and the hourhand is at h', half-way from 12 to 1. Now, if the hour-hand would stand still at h' while the minute-hand moved forward to ", half-way from 11 to 12, 27 minutes from the point 6, the hands would have the required positions; but, while the minute-hand is advancing, the hour-hand goes from h' to h; .. the minute-hand must stop at i, as much short of as his in advance of h'; i. e. the hour and minute hands together move over the space represented by 27 minutes on the dial; but the hour and minute hands together move over 13 spaces while the minute-hand alone moves over 12 spaces; hence the proportion; 13: 12 : 27 m. : 25 m., the number of minutes beyond half-past 12 when the hands will have the required positions. It 6 ST 134. At what time between 5 and 6 o'clock do the hour and minute hands make equal acute angles with the line from 12 to 6? 135. At what time between 2 and 3 o'clock do the hour and minute hands point in opposite directions? 136. At a certain time between 8 and 9 o'clock the minutehand was between 9 and 10. Within an hour afterwards the hour and minute hands had exchanged places. What was the 1st mentioned time? 137. What number is that which, being increased by 3 of of 10 and the sum diminished by 7, will give a remainder of 93? 138. If 20 boys will perform as much labor as 15 men, and 12 men as much as 18 women, how many boys would be required to perform as much labor as 27 women? |