Problems for Arithmetic or Algebra 1. When a boy had walked five times around a pond and 75 rods more, he had walked 5 miles. How far is it around the pond? 2. Robert's age is of his father's age. Three times his age added to his father's age would make 88 years. What is the age of each? 3. If 5 is taken from three times a certain number, of the remainder will be 15 less than twice the number. Find the number. 4. If a certain number is taken from 30, and the remainder is subtracted from three times the number, this remainder will be 2 more than twice the number. is the number? 5. A farmer bought an adjoining farm his original farm, and another which was original farm. He then had 380 acres. his original farm? What as large as as large as the How large was 6. The length of a rectangular lot is 7 times its width. It contains 9 acres 135 square rods. What is the width? 7. Find the dimensions of a block of granite in the form of a square prism whose length is 5 times the width, or thickness, and which contains 1080 cubic inches. 8. Find a mean proportional between 8 and 32. 9. Find the length of a square field which is equal in area to two fields, one of which is 50 rods long and 20 rods wide, and the other 40 rods long and 15 rods wide. 10. If $40 will gain $2.30, how much will $67 gain in the same time and at the same rate? 11. It takes 7 yards of lining for 12 yards of cloth which is 30 inches wide. How wide is the lining? 1. What is the average of the numbers 9, 15, and 18? 2. What is the average of the numbers 85, 93, 76, 641, 82, 891, and 993 ? 3. The average of five numbers is 10. To what is the average reduced by combining with these five numbers the numbers 6, 7, and 9? 4. A school contains 20 boys and 15 girls. The average age of the boys is 16 years, and that of the girls 13 years. What is the average age of all together? 5. If I mark goods, which cost $1.20, so as to gain 331%, and afterward sell them at 50% less than the marked price, what per cent of the cost do I lose? 6. If I mark goods, which cost $2, so as to gain 20%, and afterwards mark them again 20% above the first marked price, what per cent do I gain on the cost by selling at the second marked price? 7. I bought a bill of goods at 10% below the marked price, and paid $67.50. What was the marked price? I re 8. I bought a bill of goods at 10% below the marked price, and had to sell them at 10% below the cost. ceived $81. How much did they cost me? 9. What was the marked price? 10. Find the surface of a sphere whose diameter is 8 inches. 11. Find the volume of a sphere whose diameter is 15 inches. 12. Find the surface of a sphere whose circumference is 31.416 feet. 13. Find the volume of a sphere whose circumference is 314.16 feet. 1. Find 121% of 9240. 6. 15 is what per cent of 90? 11. 45 is 5% of what number? 12. 63 is 31% of what number? 16. What is 15% more than 50? 21. What number increased 50% equals 30? 22. What number decreased 10% equals 81? 23. What number increased 121% equals 225? 24. What sum increased 6% equals $42.40? 25. What sum decreased 7% equals $418.50? Similar Forms The areas of similar plane figures are to each other as the squares of their corresponding dimensions. The volumes of similar solid bodies are to each other as the cubes of their corresponding dimensions. The ratio of the area of a 3-inch square to that of a 6-inch square is not the same as the ratio of 3 to 6, but as the ratio of the square of 3 to the square of 6, or as 9 to 36. The volume of a sphere whose diameter is 2 feet is to the volume of another whose diameter is 5 feet as the cube of 2 is to the cube of 5, or as 8 is to 125. 1. The lengths of 2 squares are 1 foot and 2 feet. How do the areas of the squares compare with each other? 2. The diameters of 2 circles are 3 feet and 5 feet. What is the ratio of their areas ? 3. How many 2-inch cubes are equal in volume to a 6-inch cube? 4. What is the ratio of the entire surface of a 3-inch cube to the entire surface of a 4-inch cube? 5. The end of a square prism is 5 inches square, and its length is 12 inches. What is its entire surface? 6. What is the entire surface of a square prism similarly shaped, which is 20 inches long? |