125. If a grocer's scales give only 15 ounces for a pound, out of how much money does the grocer cheat a customer who buys tea to the amount of $16? 126. If of a bushel of corn is worth of a bushel of wheat, and corn is worth $0.63 a bushel, how much wheat can be bought for $24.50? 127. A man paints two sides of a board-fence, 6 feet high, in 5 days, working 10 hours a day. If he can paint 8 square yards an hour, how long is the fence? 128. For what principal must I write a note on 4 months, at 7%, to enable me to receive at a bank, on its date, $300? 129. Find the cube root of 4436184. 130. How many cubic yards of earth must be thrown out to dig a ditch 2 feet deep and 3 feet wide, just within the boundary of a garden 16 rods long and 12 rods wide? 131. A and B engage in trade. A puts in $10000 and at the end of 5 months takes out a certain sum; B puts in $ 6000 and after 3 months puts in $ 4000 more; at the end of the year A's gain is $1800 and B's $2250. What sum did A withdraw at the end of 5 months? 132. What number multiplied by of itself will give 54? 133. If 24 men, in 9 days of 12 hours each, build a wall 200 feet long, 6 feet high, and 2 feet thick, how many men, in 72 days of 10 hours each, can build a wall 950 feet long, 8 feet high, and 5 feet thick? 134. If on February 20 I buy $10000 United States 6 % bonds at 1104, and $10000 City of Chicago 7's at 103, and accrued interest from January 1 on the latter, what will they cost me? 135. A certain savings bank pays 5% a year, adding the accrued interest to the principal at the end of each 6 months, and in it Mr. J. deposits every six months $20 on the day when interest begins. What sum will stand to his credit in the bank on the day after he makes his sixth deposit ? 136. A room 15 by 20 feet is to be carpeted with tapestry carpet, of a yard wide. In order to make the figure match a breadth cannot be split, and if the breadths are laid to run lengthwise of the room, each breadth must be 10 inches longer than the room, and if the other way, 8 inches. What is the least number of yards of this carpet that must be bought to carpet the room, and what will it cost at $0.95 a yard? 137. How many more yards of carpet must be bought to carpet the room named above than to carpet a room whose floor contains the same number of square feet, but is so shaped that none of the carpet needs to be turned under? 138. Sold to Luther Farwell goods as follows : Jan. 17, 1894, on 6 m., 275 yd. cloth, @ $2 When ought the balance of this account to begin to draw interest? 139. If I deposit, on the day when interest begins, $200 in a savings bank that pays 6% a year, adding the accrued interest at the end of each 6 months, what sum will stand to my credit at the bank the day after I make my eighth deposit? 140. How large a square floor can be laid with 2704 square feet of boards? 141. Find the square root of the square root of 16 times 81. 142. What is the square root of 9 times the square of 12? 143. A rectangular piece of land containing 25 acres has its length to its breadth as 4: 3. Find the length and the breadth. 144. What is the side of a square equivalent to a rectangular field that is 121 rods long and 64 rods wide? 145. How many feet of fence would be required to enclose an acre of land in the form of a square? 146. What is the length of one side of a square field containing 15 acres and 1 square rod? 147. If it costs $312 to enclose a field 216 rods long and 24 rods wide, what will it cost to enclose a square field of equal aren with the same kind of fence? 148. I hold three notes bearing interest from date: the first, dated July 3, 1894, is $530; the second, dated Oct. 9, 1894, is $740; the third, dated Feb. 6, 1895, is $630. If a single note of $1900 is substituted for these three, when ought it to be dated? 149. A person owes a debt of $1680, due in 8 months, of which he pays in 3 months, in 5 months, in 6 months, When is the remainder due ? and in 7 months. 150. If I buy $1200 worth of goods, half on 2 months' and half on 4 months' credit, what can I afford to pay at the time of purchase, if money is worth 6% ? 151. A note of $1250, dated July 5, 1892, was paid June 6, 1894, with interest at 8%. What was the amount paid? 152. If 15 men, working 10 hours a day, can do a certain piece of work in 18 days, how many days will it take 13 men to do the same work by working 8 hours a day? 153. In what time will $ 800 at 8 % gain $ 150? 154. What is the present worth of $1609.30, due in 10 months 24 days, when money is worth 5% ? PRACTICAL EXAMPLES. 504. The following examples are arranged according to subjects, and are to be selected from at discretion. PROPERTIES OF NUMBERS. 1. What are the prime factors of 1440? 6. Is 991 prime? 7. Is 2501 prime? 8. What is the greatest common divisor of 12, 16, 84, and 144? 9. What is the greatest common divisor of 1181 and 2741? 10. Find the greatest common divisor of 340200, 583200, and 2268000. 11. What is the least common multiple of 25, 75, 100, 10, 5, 200, and 150? 12. Find the least common multiple of 8, 12, 72, 92, and 364. 13. Find the least common multiple of 5, 10, 12, 20, and 36. 14. Multiply the greatest common divisor of 18, 45, 63, and 99 by their least common multiple. 15. What is the smallest sum of money that can be made up of 2-cent, or 3-cent, or 5-cent, or 10-cent, or 25-cent pieces? 16. A can walk round an island in 12 days, Á in 16 days, and C in 20 days. If they start at the same time from the same point and walk in the same direction, in how many days will they all come together again, and how many times will each have walked round the island? 17. A can hoe a row of corn in a certain field in 30 minutes, B can hoe a row in 20 minutes, and C can hoe a row in 35 minutes. What is the least number of rows that each can hoe in order that all may finish together? COMMON FRACTIONS. 18. Reduce 33828 to its lowest terms. 19. Reduce 1998 to its lowest terms. 20. Find the greatest common divisor of both terms, and reduce the fraction 945 to its lowest terms. 4620 21. Reduce 2, 128, 76, and 27 to fractions having the least common denominator. 48 22. Reduce, 7, 14, and to fractions having a common denominator. 23. Reduce,, 21, 1% to fractions having a common denom inator. 24. Find the sum of 43, 53, 17, and 1422. 28. Reduce of } of }} of 11⁄2 of 83 to its simplest form. 29. Divide of 18 by 1 of 3§. 30. Find the product of 33 × 2 × 43 × 5. of 5 of 73 31. Reduce to its simplest form. 1214 |