PROBLEMS. How many 1. A man has 12,000 dollars to invest in land. How many acres can he buy at 125 dollars an acre ? 2. There are 47,520 yards in 27 miles. How many yards are there in one mile ? 3. There are 640 acres in a square mile. square miles are there in the District of Columbia, which contains 38,400 acres ? 4. If the earth in its revolution round the sun moves 1,611,600 miles a day, how far does it move in one second, a day containing 86,400 seconds? 5. If 4671 building lots are worth 1,985,175 dollars, how much is one building lot worth? 6. What number of dollars must be multiplied by 124 to produce 40,796 dollars ? 7. There are 31,173 verses in the Bible. How many verses must be read each day, that it may be read through in a common year? 8. Pennsylvania contains 45,125 square miles, and Delaware contains 2050 square miles. How many states the size of Delaware could be made from Pennsylvania ? 9. How long can 125 men subsist on an amount of food that will last one man 4500 days ? 10. If 1988 hogsheads of molasses cost 115,304 dollars, what will one hogshead cost? 11. A balloon is said to have ascended 37,000 feet. How many miles? (One mile = 5280 feet.) 12. If one of two factors of 4,312,695 is 1205, what is the other factor? 13. A man has 8000 dollars; he buys two houses for 4500 : dollars, and invests the remainder in land at 140 dollars an How many acres of land can he buy? acre. 14. If the distance from the earth to the sun is 91,430,000 miles, how long will it take light from the sun to reach us, if it moves 186,000 miles a second ? 15. How many years will it take a man to save $5475, if his savings average one dollar per day, reckoning 365 days to the year? а 16. A railroad that cost $4,076,500 was divided into 8153 equal shares. What was the cost of each share ? 17. There are 231 cubic inches in a gallon. How many gallons in a tank that contains 139,755 cubic inches? 18. The salary of the President of the United States is $50,000 a year. How much does he receive each day? 19. If a pound of cotton can be spun into a thread 70 miles long, how many pounds of it must be spun to reach around the world, a distance of 25,000 miles ? 20. Two trains on the same railway are 689 miles apart. If they start at the same time and run toward each other, one averaging 27 miles per hour, and the other 26 miles, in how many hours will they meet ? 21. Find the value of 15 X 37,153 — 73,474 – 67,152 + 4 + 40,734 X 2. Suggestion : Use X and -- first. 22. Find the value of (7854 – 4913) X 3 – (20,352 – 5194) · 53 — 6+ (395,456 — 2364) — 556. : 23. Find the value of (12 + 7 – 9) X 5 = 10. 24. Find the value of (5 + 7 — 3) X 3 + (3 + 5 — 4) 25. Find the value of (828 — 475 — 325) + (982 – 620 - 82). 26. Find the value of 849 X4 : 3 - 714 X 4 : 3
135 x 4 : 3. 27. Find the value of (LI. – III. + I.) – VII. + (III. XV. - IX.) - III. – • 28. Find the value of (XXVII. + XXII. - XIX) X VI. . 29. Find the value of (CCCLXI. — CCI.) x (CCCXX. - X CCCXII.). 30. Find a second factor of 4807, taking 11 as the first factor. MISCELLANEOUS EXERCISES. 1. The minuend is 900,000 and the subtrahend is 323,456. What is the difference ? 2. The minuend is 300,400 and the difference 197,325. Find the subtrahend. 3. The subtrahend is 204,054 and the difference is 9735. What is the minuend? 4. The product of two numbers is 567,204, and one of the numbers is 141,801. Find the other number. 5. The multiplier is 3007 and the multiplicand is 3007. What is the product ? 6. The product is 24,483 and the multiplier is 3. What is the multiplicand ? 7. The product is 24,402 and the multiplier is 21. Find the multiplicand ? 8. The product is 20,692 and the multiplicand is 739. Find the multiplier. 9. The divisor is 437, the quotient is 730, and the remainder is 89.. What is the dividend ? 10. The divisor is 954, the quotient is 840, the remainder 227. Find the dividend. 11. What number divided by 573 will give a quotient of 205 and a remainder of 89 ? 12. Of what number is 623 both the divisor and the quotient? 13. The sum of two numbers is 21,000,000; one of the numbers is 12,113,141. Find the other number. 14. Divide 18,490,700 by 73,000. 15. Multiply 5690 by 3008. Prove by division. 16. Show that (26 x 26 – 15 X 15) = (26 + 15) = 26 - 15. 17. How many times in succession can 3589 be subtracted from 241,462? What will be the remainder ? 18. A certain number is contained 41 times in 1043, with 18 as a remainder. What is the number? 19. What number is that which, divided by 12, the quotient multiplied by 8, and 580 added to the product, equals 740? 20. Divide 9,999,999 by 33,300. MISCELLANEOUS PROBLEMS. 1. If a ship sails 10 miles an hour, in how many days will it cross the Atlantic Ocean, 2880 miles ? a Process Indicated. 2880 : 10 the number of days required. 24 = Process. Explanation. 2880 1. Since the ship sails 10 miles an hour, = 288 hours. 10 it will sail 2880 miles in 2880 : 10 = 288 hours. 24) 288 (12 days. 2. Since 24 hours 1 day, 288 hours 24 288 48 days 12 days. 24 48 NOTE.--Carefully indicate each solution. 2. How many barrels of apples, at $2.75 a barrel, must be given for 6 barrels of cranberries, at $8.25 a barrel ? 3. How many pounds of coffee, worth $.12 a pound, must be given for 368 pounds of sugar, worth $.09 a pound? 4. A young farmer earns $60 a month and spends $25. In what time can he save enough to pay for a farm of 50 acres, at $28 an acre ? 5. A grocer bought 250 pounds of coffee for $82.50, and sold it at $.37 a pound. What did he gain? 6. (309 — 76) + (4426 — 309) + (6375 4426) + 76 = 9375 is a defective equation to what extent? 7. There were 24,012 public schools in Pennsylvania in 1893, with 994,407 pupils. How many pupils, on an average, in each school? 8. Multiply the sum of 276 and 347 by three times their difference? 9. A park is 48 rods long and 32 rods wide. How many times must a boy go around it on his bicycle to travel 45 miles, there being 320 rods in a mile? How many times must he go around the park to travel one mile? 10. A man dying, left three tracts of land to be divided equally among his six children. The first tract contained 1118 acres; the second, three times as much lacking 193 acres; the third, twice as much as the other two lacking 105 acres. What was each one's share ? 11. A.'s house cost $7825, which was $4218 less than the cost of the farm. What was the cost of both ? 12. The diameter of the earth at the poles is 41,707,620 feet, and at the equator, 41,847,426 feet. How much does the equatorial diameter exceed the polar diameter ? 13. What will 53,000 bricks cost at $7.25 per M.? 14. Mr. Gill, a drover, purchased 36 head of cattle, at $64 a head, and 88 sheep, at $5.00 a head. He sold the cattle for $40.00 a head, and the sheep for $4.00 apiece. Did he lose, and how much ? 15. Of two boys, one was lazy and did not rise till nine o'clock, while the other was active and rose every morning at six. Allowing 365 days to the year, how many hours did the lazy boy lose in five years ? 16. There are two numbers, the greater of which is 25 |