(a) Find the sum of the first five results. What % is 16. $.76 of $38 ? 17. $9.02 of $225.50? 22. $21 of $175 ? (What is one % of $38?) (What is one % of $754?) (What is one % of $175?) 23. A sold goods for B to the amount of $346.25; he received as his commission for selling the goods, $41.55. His commission was what per cent of the sales? 24. C collected for D $643.50; he retained as his commission for collecting the money, $38.61. His commission was what per cent of the sales? 25. F purchased 256 barrels of apples; he lost by decay a quantity equal to 16 barrels. What % of his apples did he lose? Algebra. 216. PROBLEMS LEADING TO EQUATIONS CONTAINING FRACTIONS. If to of Bernie's money you add of his money the sum is $63. How much money has he? 1. If to Thus we find that Bernie had 108 dollars. of a certain number you add of the same number, the sum is 45. What is the number? of 2. A lady upon being asked her age replied: If from my age you subtract of my age the remainder will be 9 years. How old was she? 3. The sum of two numbers is 72, and the less number equals of the greater number. What are the numbers? ៖ Let x = the greater number. 4. The sum of two numbers is 75, and the less number equals of the greater number. What are the numbers? 5. The difference of two numbers is 30, and the less number equals of the greater number. What are the numbers? * Observe that the equation might have been cleared of fractions by multiplying both its members by 12, the 1. c. m. of 3 and 4. Algebra. 217. MISCELLANEOUS PROBLEMS. 1. Harry has some marbles; Joseph has 8 more than as many as Harry; together they have 68. How many has each? 2. William has 12 more than as many cents as Lucius; together they have 87 cents. How many cents has each ? 3. If to the half of a certain number you add a third of the number, the sum will be 5 more than 3 fourths of the number. What is the number? 4. If to of a number you add of the same number, the sum will be 12 more than of the number. the number? What is 5. If to a certain number you add 5 times the number, the sum will be 24 more than 4 times the number. is the number? 6. If to will be a. What of a number you add of the number the sum What is the number? Observe that you may put in the place of a any number you please ; hence any number is g of the sum of its half and third. 1. Draw a rhombus. Make the angle a, 110°. Use the protractor for measuring the angle a only. Make ab and ac each 2 inches. Then draw bd parallel to ac and cd parallel to ab. Prove your work by measuring the other angles. Observe that when one side and one angle of a rhombus are given the rhombus may be drawn. 2. If the angle a of a rhomboid is 110°, how many degrees in angle b? In angle c? In angle d? 3. Draw a trapezoid. Make the side ab 3 inches long. Make the angle a, 110 degrees, and the line ac 2 inches long. Make the angle b, 90 degrees; and the line bd of indefinite length, but long enough to form the side bd. Draw cd parallel to ab. Prove the work by finding the sum of the four angles. 4. Draw a trapezium. Make the angle a, 100°; the line ab 3 inches long, and the line ac 2 inches long. Make the angle b, 120°, and the side bd of indefinite length. Make the angle c, 85°. Angle d should be an angle of how many degrees? Prove the work by measuring angle d. 5. Draw four lines that together make a very irregular trapezium; then using the protractor, find the sum of the four angles. 219. Miscellaneous Review. 1. If I lose of my money, what % of my money do I lose ? 2. Mr. Button spent $5 of the $12 which he had earned. What per cent of what he earned did he spend ? 3. Mr. Thomas earns $150 per month. The monthly rent of the house in which he lives is equal to 15% of what he earns. How much is his rent per year? 4. Mr. Jones purchased 500 barrels of apples. He lost by decay a quantity equal to 75 barrels. What per cent of the apples purchased remained sound? 5. Mr. Brown borrowed $625. He used 87% of this money to pay debts. How much of the money borrowed did he have left? 6. Mr. Green paid $24.60 for a suit of clothes. If this was exactly 15% of his monthly earnings, how much does he earn per month? 7. Mr. White earns $1500 per year. He spends $312 for board, $200 for clothes, $75 for books and papers, $80 for traveling and amusements; gives to his church $40, for charitable purposes, $35, and all his other expenses amount to $23. The remainder of his salary he puts into a savings bank. What per cent of his salary does he save? 8. If to of my money you add 16 of my money the sum will be $63. How much money have I? 9. The sum of two numbers is 120, and the less number is of the greater. What are the numbers? 10. If one angle of a rhomboid is 80°, what is the size of each of the other angles? 11. Three twenty-fifths is what % of ? |