18. In what time will $6, on interest at 5 per cent., gain 70 cents? Solution. $6, at 5 per cent., gains 30 cents in 1 year; 30 cents in 70 cents, 2 times; therefore, $6, at 5 per cent., will gain 70 cents in 2 years, or 2 years and 4 months. 19. In what time, at 6 per cent., will $10 gain $3? 20. In what time, at 10 per cent., will $100 gain $25? 21. In what time, at 4 per cent., will $4 gain 24 cents? 22. In what time, at 8 per cent., will $50 gain $23? 23. In what time, at 5 per cent., will a given principal double itself? Solution. Any principal, at 1 per cent., will double itself, i. e. it will gain 100 per cent., in 100 years; and at 5 per cent., in of 100 years, viz., 20 years. 24. In what time, at 4 per cent., will any principal double itself? In what time, at 6 per cent.? At 8 per cent.? At 20 per cent.? At 25 per cent. ? At 2 per cent.? At 50 per cent.? At 12 per cent.? At 64 per cent.? At 163 per cent.? At 333 per cent. ? LESSON IV. 1. WHAT principal, at 6 per cent., will gain 36 cents in 1 year and 6 months? Solution. $1, at 6 per cent., gains 9 cents in 1 year and 6 months; 9 cents in 36 cents, 4 times; therefore, $4, at 6 per cent., will gain 36 cents in 1 year and 6 months. Or, since the interest of any sum for 1 year and 6 months, at 6 per cent., is 8 of the principal, it follows that 36 cents is 8 of the required principal; hence, of 36 cents, or 4 cents, is Too, and 188 is 100 times 4 cents, which is 400 cents, or $4; therefore, etc. 2. What principal, at 5 per cent., will gain 60 cents in 2 years? 3. What principal, at 8 per cent., will gain $2 in 6 months? 4. What principal, at 10 per cent., will gain $15 in 1 year? 5. What principal, at 8 per cent., will gain $60 in 3 years and 9 months? 6. What principal, at 10 per cent., will amount to $6.60 in 1 year? Solution. The amount of $1 for 1 year, at 10 per cent., is $1.10; $1.10 in $6.60, 6 times; therefore, $6, at 10 per cent., will amount to $6.60 in 1 year. Or, the interest of any sum for 1 year, at 10 per cent., is of the principal, and this added to the principal, 18, makes the amount = 13 of the principal; hence, $6.60 is of the principal, and of $6.60, or 60 cents, is, and 18, or the whole principal, is 10 times 60 cents=600 cents, or $6; therefore, etc. 7. What principal, at 5 per cent., will amount to $22 in 2 years? To $44 in 2 years? 8. What principal, at 8 per cent., will amount to $58 in 2 years? To $84 in 11⁄2 years? 9. What principal, at 4 per cent., will amount to $66 in 5 years? To $280 in 10 years ? 10. What principal, at 12 per cent., will amount to $250 in 2 years? To $121 in 3 years? 11. What principal, at 163 per cent., will amount to $42 in 1 year? To $80 in 2 years s? 12. What principal, at 6 per cent., will amount to $10.60 in 1 year? To $21.80 in 1 year and 6 months? 13. What sum can I obtain at a bank for a note of $80, payable in 60 days? Solution. The interest of $80 for 60 days is 80 cents, which, taken from $80, leaves $79.20; therefore, etc. 14. What sum can I obtain at a bank for a note of $48, payable in 45 days? What sum for a note of $64, payable in 75 days? SECTION NINTH. LESSON I. 1. BOUGHT 2 lb. of figs, at 20 cents per pound, and gave in payment a quarter of a dollar, a dime, and the rest in cents; how many cents did I give? 2. I have a rectangular field 20 rods long and 15 rods wide; what will it cost to build a wall around it, at $1.50 a rod? 3. I have a field containing 3 roods and 10 rods, what is it worth, at $2 per square rod? 4. What is the cost of a load of wood which measures 1 cord and 2 cord feet, at 75 cents per cord foot? 5. How many days from July 4th, at 9 o'clock in the morning, to Aug. 10th, at 9 o'clock in the evening? 6. What cost 3 score bushels of corn, at of a dollar a bushel? 7. If a ship sail 180 miles each day, how far does she sail in a week? 8. Bought a load of wood which measured 9 cord feet; of the load was pine, at $4 a cord, and the rest was oak, at 75 cents a cord foot; what was the cost of the load? 9. What cost 10 10. I have a square which is 22 eet long; piece? acres of land, at $20 per acre ? piece of land each side of how many rods is it round this 11. If it takes 16 yards of silk to make a dress, what will the silk for 2 dresses cost, at 1 dollars per .yard? 12. I have a rectangular garden which is 12 rods long and 7 rods wide; how many square rods does it contain ? 13. Mr. Smith has a rectangular garden, 6 rods wide, and containing 48 square rods; how long is it? 14. Mr. French has a rectangular garden 10 rods long and containing 70 square rods; how wide is it? 15. A man bought a share of the Boston and Maine Railroad stock for $100, and sold it for $103; what per cent. on the purchase money did he gain? 16. A grocer bought a box of sugar for $12, and sold it so as to gain 5 per cent.; how much did he gain? 17. A merchant bought a piece of silk for $75, and sold it so as to gain 10 per cent.; how much did he gain? What did he receive for the silk? 18. A shoedealer bought boots at $4 a pair, and sold them at $5; what per cent. did he gain? He bought others at $5, and sold them at $4; what per cent. did he lose? 19. A grocer bought molasses at 40c. per gallon ; how shall he sell it to gain 25 per cent.? 20. A merchant bought goods for $50; but, they being damaged, he is willing to lose 20 per cent.; for what sum is he willing to sell them? 21. A laborer agreed to work 5 months for 60 dollars; how much did he receive for a month? How much for a week, allowing 4 weeks to the month? How many shillings a day, allowing 6 working-days to the week? 22. If a melon is worth 8 oranges, how many melons are 44 oranges worth? 23. A man sold 24 hens at the rate of 3 for a dollar; how many dollars did he receive? 24. If wine is worth 24 cents a pint, what is 1 giï worth? What are 3 gills worth? 25. At 80 cents a bushel, what is a peck of corn worth? What is a half peck worth? 26. Five boys bought a slcd for 90 cents, and sold it for 75 cents; sharing the loss equally, what did each boy lose by the bargains? 27. A man paid $35 for wood, at $7 a cord; how many cords did he buy ? 28. A man paid $63 for 9 cords of wood; what was the price per cord? 29. A hound is 36 rods behind a fox, and both are running in the same direction; but the hound gains upon the fox 3 rods in a minute; in how many minutes will the hound overtake the fox? 30. A fox is 48 rods from a hound, and running 80 rods per minute; but the hound is pursuing him at the rate of 83 rods per minute; how many minutes can' the fox run before the hound overtakes him? 31. What will 9 quarts of milk cost, if 6 quarts cost 24 cents? 32. A cask containing 56 gallons, has a pipe which discharges 8 gallons per minute; in how many minutes will the cask be emptied? 33. There is an empty cask that will hold 84 gallons, and, by a pipe, 12 gallons run into it in a minute; in how many minutes will the cask be filled? 34 An empty cask, that will hold 48 gallons, receives 10 gallons per minute by one pipe, and discharges 6 gallons per minute by another pipe; how many gallons remain in the cask in one minute? In what time will the cask be filled? 35. A vessel which contains 63 gallons of water, discharges 12 gallons per minute by one pipe, and receives 9 gallons per minute by another pipe; in how many minutes will the vessel be emptied ? 36. If 1 man can do a piece of work in 42 days, in how many days can 7 men do it? In how many days can 12 men do it? 37. If 1 man can do a piece of work in 55 days, how many men can do the same in 5 days? 38. A man can do a piece of work in 66 hours; in how many days can he do it if he works 11 hours each day? 39. A man can do a certain job in 56 hours; how many hours a day must he work to do it in 7 days? |