6. How many perches of stone are required to wall a well 50 ft. deep, if the wall is 1 ft. thick and the well is 4 ft. in diameter in the clear? 7. What will be the cost of digging and walling the cellar of a house 24 ft. by 32 ft., the cellar being 5 ft. deep and the wall 8 ft. high and 18 in. thick, if the digging cost 50 cents a cubic yard and the masonry $4 a perch? MISCELLANEOUS PROBLEMS. 1. A gardener has a flower-bed 8 ft. long and 6 ft. wide, and wishes to make a board-walk around the outside 4 ft. wide; what will it cost at 3 cents a square foot? 2. A farmer has an acre of land 5 ch. long and 2 ch. wide: he wishes to make a tight board fence around it 5 ft. high; what will the boards cost at 2 cents a square foot? 3. What will it cost to dig a trench 40 rd. long, 18 in. wide, and 2 ft. deep at 10 cents a cubic yard? 4. What will it cost to dig a well 7 ft. in diameter and 42 ft. deep at 50 cents a cubic yard? 5. How many square yards of zinc will be required to line a cylinder 8 ft. in diameter and 40 ft. high, including both ends? 6. How many acres of land in a triangular field whose base is 120 rd. and altitude 80 rd.? 7. Mr. White has a rectangular farm which contains 92 acres; how many rods of fence will be required to enclose it if the width is 20 chains? 8. How much more will it cost to fence a field 20 rd. wide, and containing 40 acres, than to fence a square field of equal area 80 rods on a side, if the fence costs $2 a rod? 9. How many boards 16 ft. long and 15 in. wide will be required to weather-board a barn 80 ft. long, 50 ft. wide, and 20 ft. to the eaves if the two gable ends are 13 ft. high? 10. How many cubic yards of earth must be removed to dig a cellar 40 ft. long, 30 ft. wide, and 6 ft. 5 in. deep? 11. How deep must a cistern 6 ft. in diameter be to contain 40 hhd.? 12. How many cubic feet in a cistern which contains 100 hhd.? 13. A druggist buys 20 lb. of drugs by avoirdupois weight at $10.50 a pound, and sells them at the rate of $1.05 an ounce apothecaries' weight; what is his gain? 14. A man weighs 175 lb. avoirdupois; how much would he weigh by Troy weight? 15. A wagon 8 ft. long and 4 ft. wide is piled with wood to a depth of 6 ft; what is the cost of the wood at $8.10 a cord? 16. If a vessel holds 600 gallons of water, how many bushels of grain can be put into it? 17. If 5 bushels of seed will sow an acre, how much seed will be required to sow a rectangular piece of land 125 ft. long and 50 ft. wide? 18. How deep must a bin be that is 8 ft. long and 6 ft. 6 in. wide to hold 200 bushels of wheat? 19. Find the cost of 50 white-pine joists, each 16 ft. long, 7 in. wide, and 4 in. thick, at $28 per M. 20. Find the cost of a plank-walk 100 ft. long, 5 ft. 3 in. wide, and 2 in. thick, at $15.50 per M. 21. How many perches of stone will be required to build a monument 120 ft. high and 20 ft. square, with a cylindrical opening through the centre 8 ft. in diameter ? 22. If a cubic foot of water weighs 1000 oz., what is the weight of 15 hhd. of water? 23. An irregular stone was thrown into a cylinder 2 ft. 6 in. in diameter, partly filled with water: when the stone was immersed in it, the water in the cylinder rose 10 in.; find the contents of the stone. 24. A circular lake 3 chains in diameter has a walk 8 ft. wide around it; what is the area of the walk? 25. The distance around a circular park is 2 miles; how many acres does it contain? 26. How many bricks are required to build the walls of a house 32 ft. long, 28 ft. wide, and 24 ft. high, the gables being 12 ft. high and the walls 17 in. thick, if there are 24 windows 2 ft. 10 in. by 6 ft. 2 in., and 5 doors 3 ft. 4 in. by 8 ft. 6 in.? 27. What will be the cost of laying the bricks of the preceding problem at $3.50 a thousand, if an allowance ofis made for doors, windows, and corners? 28. M and N buy a piece of land containing 14 A. 120 P. for $2380; how much land should each receive, if M pays $952 and N the remainder? 29. If gold is worth $21.50 an ounce Troy, what is the value of a piece of gold weighing 20 lb. 10 oz. avoirdupois ? 30. The longitude of Constantinople is 28° 49′ east, and of St. Paul 93° 5' west; what time is it at Constantinople when it is midnight at St. Paul? 31. The forward wheels of a wagon are 13 ft. 4 in. in circumference, and the hind wheels 18 ft. 6 in.; how many more times will the forward wheels revolve than the hind wheels in going from Philadelphia to New York, a distance of 90 miles? 32. If a piece of metal is 10 in. wide and 4 in. thick, what length of it will be required to make 8 cu. ft.? 33. If 8 T. 12 cwt. 45 lb. of iron cost $517.35, how much will 12 T. 11 cwt. 42 lb. cost at the same rate? 34. R owns a piece of land which is 80 ch. 42 li. long and 60 ch. 36 li. wide; how many acres does it contain? 35. Mr. Taylor's house is 36 ft. long and 32 ft. wide: the roof projects 6 in. on each side and 14 in. at the ends, and all the water falling on the roof is conducted to a cistern 7 ft. in diameter; to what depth would it be filled by a shower in which 1 in. of rain fell? SECTION VIII. PERCENTAGE. ORAL EXERCISES. 151.-1. A FARMER planted 200 trees, and 1 out of each hundred died; how many trees died in all? If 2 out of each hundred had died, how many would have died in all? If 3? If 4? If 5? If 6? 2. If 7 trees out of each hundred die, what part of them die? If 9 out of each hundred die? If 11? If 13? If 17? If 25? If 50? If 75? If 100? These expressions, 7 hundredths, 9 hundredths, 11 hundredths, etc. of a number are called Per Cents., from the Latin per centum, which means by the hundred. 3. What per cent. of a number is 3 hundredths of it? 5 hundredths? 6 hundredths? 8 hundredths? 9 hundredths? 12? 15? 18? 20? 25? .06? .09? .12? .18? .45? .80? .85? .90? .94? 16 00 20 per 4. How many hundredths of a number is 6 per cent.? 8 per cent.? 9 per cent.? 10 per cent.? 12 per cent.? cent.? 90 per cent.? The symbol % is generally used instead of per cent. Thus, 5% means 5 per cent. 5. How many hundredths of a number is 7%? 14%? 15%? 6%? 5%? 50%? 75%? 80%? 100%? 152. To express a per cent. as a decimal and as a common fraction. Any per cent. of a number may be expressed as a decimal or as a common fraction. Thus, Express each of the following as a decimal and as a com mon fraction in its lowest terms: 153. To express a common fraction as a per cent. Any common fraction may be expressed as a per cent. by reducing it to hundredths. Thus, Express each of the following fractions as a per cent.: |