134 PROBLEMS-SILKWORM CULTURE 1. The larva of the silkworm passes through 5 stages of about 5, 4, 5, 6, and 10 da.; what is the lifetime of a larva? 2. When a larva is full grown it spins a cocoon of silk around its body, making about 65 oscillations of its head per minute for a period of approximately 72 hours; about how many movements does it make in weaving the cocoon? 3. The silkworm moth lays about 500 eggs, of which 70% are deposited on the first day, 25% on the second, and the rest on the third; how many is this for each day? 4. After the larva stage, the worm is a chrysalis for about 20 days; it then emerges as a moth. During the next three days it lays its eggs, and lives about 12 days thereafter. Using the result of Exercise 1, find the approximate lifetime of a silkworm. 5. If the larvæ hatched from 1 ounce of eggs during the first stage require 11 lb. of mulberry-leaves, during the second stage 30 lb., during the third 120 lb., during the fourth 300 lb., and during the fifth, 1,650, how many pounds are required to mature the larvæ from 1 ounce of eggs? 6. The larvæ from 1 oz. of eggs should cover at birth 1 sq. yd. of breeding-bed. This space should be doubled twice during the second, and twice during the first stage, once during each of the third, fourth, and fifth stages; how many square yards do they occupy at last? 7. The figure represents some feeding beds or trays. According to the measurements given in the picture and the data of Exercise 6, how many trays are needed for the larvæ in the fifth stage from 1 oz. of eggs? PROBLEMS-RAINFALL 135 1. If 8 inch cubes are placed in a column, one above another, how high is the column? 2. If they are placed on a base 2 inches square, as shown in Figure 2, how high is the column? 3. If the 8 cubes are placed on a rectangular base 1 in. by 2 in., how high is the column? 4. If a dish of the size of Figure 2 is filled with water and the water is poured into a dish of the size of Figure 1, to what depth will the latter be filled? 5. If the tall dish with a base of 1 sq. in. contained 10 cu. in. and a low one had a base of 10 sq. in., to what depth would the contents of the former fill the latter? Figure 2. Figure 1. 6. The picture shows a standard rain-gage. The top is a funnel that receives the water falling on 10 sq. in. and collects it into a small tube whose base is 1 sq. in. When the water that would cover 10 sq. in. 1 in. deep is collected into a tube with a base of 1 sq. in., how high does the water stand? 7. If the water stands 5 in. in the tube to what depth would it stand, if spread over 10 sq. in.? 8. When the water stands 1 in. in the tube, to what depth would it stand if spread over 10 sq. in.? 9. What is the rainfall, or precipitation per square inch, when the water stands 2 in. in the tube? 10. Make and solve 5 other problems about the raingage. 136 Oral. REVIEW AND SUMMARY 1. What is the meaning of "per cent "? Illustrate your answer by several examples. 2. How many per cent of a number is .75 of it? .25 of it? .12 of it? .40 of it? .89 of it? .99 of it? 3. A farmer planted some corn of which 80 kernels per hundred came up; how many per cent came up? How many per cent decayed? 4. What is the symbol for "per cent"? Read: 75% of $80 = $60; 6% of $100 = $6. Written. 5. On paper ruled in squares draw a square 10 in. units on a side. Shade 1% of its area. Shade a square whose area is 25% of that of the given square. 6. Draw on the board a square 10 in. on a side. What is its area? How many square inches are there in 25% of it? In 75% of it? In 40%? In 53%? 7. Draw a rectangle 10 in. long whose area shall equal 10% of that of the square of Exercise 5; draw other rectangles each 10 in. long to equal 20%; 30%; 50%; 70% of the given square. 8. Draw a rectangle 1 inch wide whose area is 5% of that of the square of Exercise 5; draw others of the same width with areas 7%; 3%; 15%; 29% of the area of the square. How long would such a rectangle be if it equals 100% of the square? 9. To test flower-seeds, 200 seeds were planted; 40 plants sprouted; how many per cent of the seeds were good? 10. If the seeds mentioned in Exercise 9 were bought at 25¢ per ounce, what was the price of good seeds per ounce? 11. Fifty pounds of corn contain 35 lb. of starch; what per cent of corn is starch? I. Read: PROBLEMS-REVIEW 137 The receipts of the Western Union Telegraph Company during the years 1880, 1890, and 1903 were respectively: $12,782,894; $22,387,029; and $29,167,687. Their expenses for the same years were: $6,948,957; $15,074,304; and $20,953,215. 2. Write in figures: Five million, two hundred eighty thousand. Seven million three hundred seventy-one thousand, six hundred fifty. 3. Write the number of persons in your family and that in 3 other families that you know. What is the average number of persons per family? 4. Henry's age is 123 years, John's 10 years, George's 11 years. Find their average age. 5. Mary's weight is 961⁄2 lb.; James's, 823 lb.; Helen's, 102 lb.; Louise's, 8811 lb. Find their average weight. 6. The attendance at a certain school was: Monday, 621; Tuesday, 630; Wednesday, 638; Thursday, 627; Friday, 634. Find the average daily attendance. 7. During a certain period ending with 1898 England had 19 sovereigns and the average length of their reigns was 24 years; when did the period begin? 8. In 1901 the imports of Mexico from the United States were 44% of the exports to the United States; how many dollars' worth of imports did Mexico receive per $100 worth of exports to the United States? For every $500? For every $50? For every $25? 9. The foreign commerce of the United States has increased 11% since 1890; that of Africa, 49%; that of the whole world, 13%. What do these statements mean? 10. If 75% of a certain ore is copper, how many pounds of copper are there in 100 lb. of ore? In 4,000 lb. of ore? Oral. 1. 21 =- halves. 3. 52 == -fourths. FRACTIONS Mixed Numbers 5. Add 3 and 51. 4. 24-fifths. 6. Add 63 and 17. 8. Add 12g and 12 10. Subtract 9 from 17%. by 4; by 5; by 6; by 10. of a 10-hour day and sewed 11. Multiply 4 by 2; by 3; 12. A woman cut garments the remainder of the day; how many hours did she sew? Written. 13. The length of a rectangular picture-frame is 35 in. and the width 43 in; what is the area of the opening? SUGGESTION.-Reduce the numbers to improper fractions, indicate the product, and simplify by canceling. 14. A blotter is 33 in. wide and 9 in. long; how many square inches does it cover? 15. How many garments requiring of a yard of cloth can be cut from 44 yd.? SUGGESTION.-Reduce the mixed number to an improper fraction, indicate the process and cancel as usual. 16. How many packages of 33 of a pound each can be made from 63 lb. of pepper? 17. How is the work of division tested in the case of whole numbers? In fractions the product of the divisor and quotient is always the dividend. |