Review Lessons 58 to 60. 1. If both members of an equation are multiplied by the same number, is the equality of the equation changed? 2. If x represents the price of a yard of cloth, how should you represent the price of 5 yards? 3. If 5x = 20, what does x equal? 4. How many square yards are there in a ceiling x yards long and y yards wide? 6. The sum of two numbers is 234, and the larger number is 8 times the smaller. Find the larger number. 7. A and B are 64 miles apart. They travel toward each other until they meet. If A travels 3 times as many miles as B, how far will each travel? Find the value of x in the following: 14. The length of a rectangle is 3 times its width and the perimeter is 288 feet. Find the area of the rectangle. 15. A has 4 times as many cows as B, but if A should sell 6 to B, they would then have the same number. How many cows has each man? 16. A is 2 times as old as B and 3 years older than C. The sum of their ages is 72 years. How old is A? 17. A father and son earn $80 a month. If the son's wages were doubled he would receive as much as his father. How much does each receive? 18. The sum of the ages of father, mother, and son is 108 years. The mother is 3 times as old as the son, and 3 yr. younger than the father. Find the mother's age. Review Lessons 61 to 64. 1. What is ratio? 2. Compare 5 with 15. Express this ratio in three ways. 3. How many terms has each ratio? Which is the antecedent? Which is the consequent? 4. Divide $234 into two parts in the ratio of 4 to 5. 5. How long will it take 144 men to do a piece of work that 36 men can do in 16 days? = 16. 155 12:3. Is this a correct proportion? Prove your answer in two ways. 17. How many terms has a proportion? What is true of the product of the extremes and of the means? Find the missing term in the following: 27. How many bushels of potatoes will cost $12.76, when 5 bu. 2 pk. cost $4.84? 28. A and B entered into partnership. A, furnished $6000 of the capital and B $4000. At the end of the year their profits were $4800. Find each one's share. 29. Divide $2700 among three partners so that their shares shall be in the proportion of 4, 5, and 6. 30. A, B, and C engaged in business with a joint capital of $12,000. A put in $5000, B, $3000, and C, the remainder. Their profits were $4800. Find the share of each. Review Lessons 72 to 77. 1. Six times the difference between a certain number and 7 equals 12. What is the number? 2. Maine lacks 220 sq. mi. of being large enough to make 4 states the size of Massachusetts. How large is Massachusetts, if Maine contains 33,260 square miles? 3. A tree 75 ft. high was broken by the wind so that the part standing was in proportion to the part broken off as 3 to 2. How long was each part? 4. Without measuring mark off a square rod on the schoolroom floor. 5. Name some object that is about 40 rd. distant from the schoolhouse. 6. A man in an aeroplane estimated that he was 3500 ft. from the ground. What part of a mile is that? 7. How much U. S. money will it take to pay a debt in London of £85 8s.? 8. How many pounds and shillings can be bought with $194.66? 9. Some goods were invoiced at 180 lira. Find their value in U. S. money. 10. Give the rule for finding one dimension of a rectangle, when the area and the other dimension are given. 11. What must be the height of a triangle that contains 1125 sq. ft. and whose base is 90 ft. in length. 12. What is the area of a circular table top that has a diameter of 2 ft. 6 in.? 13. How many cubic feet are there in a room 35 ft. by 28 ft. by 11 ft.? How many square feet of surface are there in the room? 14. Find the entire surface of a is 4 ft. and whose altitude is 8 ft. cylinder. cylinder whose diameter Find the volume of this Review Lessons 80 to 86. 1. What is longitude? Where is the prime meridian? 2. If you travel toward the east will you find earlier or later time? 3. How do you find the difference in time between two places, when you know their difference in longitude? 4. Given the longitude of two places and the time of one place, what can you find? How will you find it? From the table of longitudes on page 82, find the difference in time between: 5. Amsterdam and New Orleans. 6. Berlin and New York. 7. Boston and Paris. 8. Canton and Rome. 9. Chicago and San Francisco. 10. Manila and Washington. 11. When it is noon at the first place mentioned in examples 5, 6, and 7, what time is it at the other place? 12. When it is 10 A.M. at the second place mentioned in examples 8, 9, and 10, what time is it at the other place? 13. A citizen of Chicago does not change the time of his watch when traveling. He went to Boston, Mass., and to San Francisco, Cal. At which place was his watch too fast? How much too fast by solar time and by standard time? How much too slow will it be at the other place? 14. The 180th meridian is called the date line. Trace this line on the globe or on a map in your geography. Crossing this line from east to west you must add a day to your reckoning. If you cross it Saturday noon you must call it Sunday noon. If you cross from west to east you must repeat a day. 15. When it is 4 A.M. at Boston, what is the solar time at San Francisco? Review Lessons 90 to 98. 1. What is compound interest? 2. State the method for finding compound interest on $500 for 4 years at 4%, compounded semi-annually. Find the difference between the simple and compound interest of: 3. $1678 for 2 yr. 5 mo. 19 d. at 6%. Using the table find the compound interest of: 7. $575 for 8 yr. 6 mo., compounded semi-annually at 4% a year. 8. $1070 for 4 yr. 3 mo., compounded quarterly at 6% a year. 9. $2040 for 7 yr. 6 mo., compounded semi-annually at 5% a year. 10. What do you mean by the convex surface of a cylinder? The convex surface is sometimes called the lateral surface. 11. How many cubic feet of gas will a tank contain that is 45 ft. in diameter and 30 ft. in height? 12. How many faces has a cube? How many has a rectangular prism? An octagonal prism? 13. Define a straight line. 14. How many straight lines or edges has a crayon box? 15. Draw two intersecting lines. How many angles are formed? 16. Measure the angles in example 15 with your protractor. Find the sum of all the angles. 17. When the hour hand of the clock is at XII, where must the minute hand be to form with the hour hand an angle of 30°? |