45. A merchant adds yearly to his capital spends $1000 each year for sundry expenses. of it but At the end of the third year his original capital was doubled. What was his original capital? 46. A trader adds yearly to his capital of it, but takes from it, at the end of each year $5000 for expenses. At the end of the third year, after deducting the last $5000, he has 1% of his original capital. Find his original apital. 47. A man bequeathed of his estate to his relatives, to a church, to a library and the balance, $16,000, to a hospital. What was the total value of his estate? 48. Find a fraction whose value is and whose denominator is 15 greater than its numerator. 49. The sum of the ages of a father and son is 85 years. If each were 5 years older, the son's age would be of his father's age. Find the age of each. 50. The length of a rectangle is 7 ft. more than its width. If the length were decreased 3 ft. and the width increased 2 ft. the area would be the same. Find its dimensions. 51. A and B together can load a car in 6 hours, B and C in 5 hours, and A and C in 4 hours. How long would it take each alone to load it? 52. The distance between Southampton and New York is 3068 nautical miles or knots. A vessel leaves New York for Southampton and sailed at the rate of 20 knots an hour. 18 hours later, a second vessel sails from Southampton for New York at the rate of 22 knots per hour. How far from New York will the vessels meet? 53. At what time, between 10 and 11 o'clock will the hands of a clock point in opposite directions? 54. A man has 10 hours at his disposal. How far can he walk at the rate of 4 miles per hour so as to return in time, riding by train at the rate of 36 miles per hour? 55. If silver loses of its weight and gold of its weight, when weighed in water, how many ounces of silver and of gold in a mass of silver and gold that weighs 476 ounces in air and 432 ounces when weighed in water? 56. The front and rear wheels of a wagon are 9 ft and 11 ft. respectively in circumference. How far will the wagon have travelled when the front wheel has made 200 revolutions more than the rear wheel? 57. A man paid a bill of $75 out of a sum he had, then deposited of the remainder in bank and had $50 left. How much had he at first? FORMULAS 87. A formula is a literal equation which expresses in algebraic symbols some rule or principle used in the solution of problems in the various sciences or in commercial life. Thus the rule for finding the interest on a sum of money, at a given rate, for a given number of years may be expressed as a formula. This formula may be used to compute interest, as follows: 1. Find the interest on $500 at 5% for 3 years and 6 mos. 2. Find the rate if the interest on $900 for 8 months is $36. Here the unknown quantity is the rate. Hence, solving the formula i = prt for the unknown quantity, Similarly, since the amount is the sum of principal and interest, if a = amount, we have the formula a = p + prt 3. In what time will $1000 amount to $1250 if put at interest at 5%? Solving the formula for the unknown quantity t, 4. Find the interest of $1250 for 3 years at 5%. 5. Find the interest of $1750 for 2 years 9 months at 5.4%. 6. Find the amount of $1000 for 6 years 7 months at 42%. 7. Find the rate if the interest on $2000 for 18 months is $125. 8. Find the time required for the interest on $2550 at 41% to be $225. 9. What principle will produce $165 interest in 2 years 5 months at 6%? 10. In what time will a sum of money double itself at 6% interest? 11. What sum at interest at 5% will produce an income of $100 per month? 12. At what rate must $50,000 be invested to produce $2000 annually? 13. In what time will $1400 invested at 41% amount to $2000? 14. The area of a triangle = base X altitude or bh, where A = area, b = base, h altitude. Find = A = the altitude of a triangle whose base is 50 ft. and whose area is 625 square feet? Note that the letters in the formulas usually represent the initials of the quantities involved. 15. What is the base of a triangle whose area is 200 square inches and whose base is 3 feet 4 inches? Solve the following formulas for each of the quantities involved: + 34. 100 32. H 1 = = = = F-32 180 ms(t2 t1). 1 1 fi + p'v' f2 = = 35. What is the total pressure (P) on the bottom of a swimming tank 50 feet square, filled with water to a depth (h) of 10 feet? Use the formula P Ahd, where A area of surface and d = weight of a unit of volume of the liquid. Water weighs 62.4 pounds per cubic foot. 36. Using the above formula, find the pressure per square foot at a depth of 3 miles in the ocean, sea water weighing 64 pounds per cubic foot. 37. If the acceleration (change of velocity per unit of time) of a marble rolling down an inclined plane is 50 centimeters per second per second, find its velocity at the end of 3 seconds from rest. Use the formula v = at. 38. Find the distance (s) the marble has covered, in problem 37, at the end of 3 seconds from rest, when s = at2. 39. A stone dropped from a bridge strikes the water 3 seconds after leaving the hand. Find the height of the bridge above the water, if the acceleration of gravity is 32.16 feet per second per second. 40. A correct Fahrenheit thermometer reading (F) of the temperature of a room is 70°. An incorrect Centigrade thermometer reading (C) in the same room is 20°. Find 180 100 shows the relations of pressure, volume and temperature of a gas. If 1000 cubic c.m. of air at 20° C. is changed in temperature to 50°C., what will be its volume, if the pressure remains constant? |
