Standard Time Refer to page 27. Give the difference in standard time and state which is earlier: 1. Between Boston and Chicago. 2. Between Boston and Charleston, S.C. 3. Between New York and Denver. 4. Between Minneapolis and Savannah. 8. From Richmond, Va., to St. Paul? 10. From Portland, Me., to Portland, Ore. ? Find the difference in longitude between each place and the line of the central meridian of the section in which it is located: 11. Omaha, whose longitude is 95° 56' 14" W. 12. New York, whose longitude is 74° 0' 3" W. 13. St. Paul, whose longitude is 93° 5′ W. 14. San Francisco, whose longitude is 122° 23' 54" W. 15. Washington, whose longitude is 77° 0' 28" W. How much earlier or later than the true time is the standard time: 16. At Boston, whose longitude is 71° 3' 48" W.? 17. At St. Louis, whose longitude is 90° 12′ 23′′ W.? 18. At Louisville, Ky., whose longitude is 85° 30' W.? 19. At Pittsburg, Pa., whose longitude is 80° 2′ W.? 20. At Portland, Me., whose longitude is 70° 15′ 18′′ W.? Percentage Review Book II., pages 212, 229. 1. Find 17 per cent of $350. 2. Find 3% of 4000 lb. 3. 17 is what per cent of 25? 4. $125 is what per cent of $500? 5. 45 is 15% of what number? 6. $72 is 41% of what sum of money? 7. $1400 is 350% of a certain sum. What is the sum? 8. 560 is 121% less than what number? 9. 791 is 13% more than what number? 10. A merchant bought a car load of bananas consisting of 850 bunches. He sold 10% of them to one man, 17% to another, and 35% to another. How many bunches remained? 11. My house is worth $7200. If I have it insured for of its value at %, what will be the amount of the premium? 12. Of 400 immigrants who arrived on a certain steamer 94 could not write. ber could not write? What per cent of the num 13. Fifteen per cent of the value of a certain stock of goods is $1252.50. Find the value of the goods. 14. By selling goods for $728 I gained 12%. What was the cost of the goods? 15. A dealer sold some flour at a loss of 20%. He lost $90. There were 150 barrels of flour. How much did it cost per barrel? 16. A commission merchant sold 60 tubs of butter the total weight of which, including the tubs, was 3315 pounds. The average weight of the tubs was 51 pounds each. He received 21 cents a pound. His commission was 5%. What sum did he remit to the shipper? Original Problems Make problems and solve them: 1. A father is three times as old as his son. 2. A farmer has a number of sheep, pigs, and hens. 3. A boy had a number of papers. and then sold some. He bought more 4. The fulcrum of a lever is between the power and the weight. 5. The weight is between the power and the fulcrum. 6. The lever is a lever of the third class. 7. The difference in time between two places is 3 hr. 15 min. 45 sec. 8. One place is 30° E. and another is 165° W. 9. The diameter of the base of a cone is 3 ft. 6 in. 10. The slant height of a cone is 4 ft. 8 in. 11. A church spire is in the form of a cone. height is 65 feet. 12. A pump handle is four feet long. 13. A board rests over a fence. each end. Its slant There is a child upon 14. A nut cracker is 9 inches long. 15. A bar 12 feet long is pushed under a stone. 16. The handles of the shears of a tinsmith are two feet long. 17. The length of an old well sweep is 18 feet. The weight upon one end is 100 lb. 18. A merchant bought a car load of oranges. 19. I had my house insured for of its value. 20. A dealer sold some flour at a gain of 10%. Algebra An expression which indicates that two numbers or quantities are equal is called an equation. The expression x+3x= 16 is an equation. x + 3x is called the first member of the equation, and 16 is called the second member. Make problems which would be represented by the following equations and solve them: 7. One half of a certain number is 17. What is the number? 8. A number added to one half of itself equals 18. What is the number? 3 x of a may be written. 1 times x or of may be written x 2 If three halves of x equal 18, what will one half of x equal? x = ? 9. Divide the number 36 into two such parts that one. part may be half as large as the other. 10. The width of an oblong is of its length. The sum of the length and width is 28 inches. How long is it? 11. The width of a rectangle is of its length. The distance around the rectangle is 20 feet. What is its area? 12. of a number and of a number equals 60. What is the number? 13. of a number less of the number equals 42. What is the number? It is evident that we may add the same number to both members of an equation, subtract the same number from both members, multiply both members by the same number, or divide both members by the same number, and still have a true equation. 1. If 3 is taken from a certain number the remainder is 9. What is the number? We wish to find the whole value of x. In other words, we wish to have x stand alone as the first member of the equation. Since the first member as it stands is 3 less than x, by adding 3 we get x for the first member. Since it is necessary also to add 3 to the second member to keep the equation true, we have x = 12. This work may be done in one step by transferring the 3 from the first to the second member and changing its sign. 2. If 5 is added to a certain number the result is 15. Find the number. To get x alone as the first member of the equation we must subtract 5 from each member. This may be done in one step by transferring the 5 from the first to the second member and changing its sign. Find the value of x in the following equations: |