EXERCISE 36 PROBLEMS WITHOUT NUMBERS 1. How do you find the discount on the list price of some goods, given the rate of discount? 2. If there is a discount series, how do you find the net price of some goods? 3. If you know the net price of some goods and the single rate of discount, how do you find the list price? 4. If you know the net price of some goods and the two rates of discount in a series, how do you find the list price? 5. If a merchant buys a bill of goods and wishes to mark the goods so as to realize a certain per cent of profit, how does he find the marked price? 6. Explain how a merchant may sell goods at a certain per cent below the marked price and still make a profit. 7. If you know the marked price of some goods and the per cent of profit, how do you find the cost? 8. How do you find a commission merchant's commissions on the sale of produce sent him to sell? 9. If you know the rate and amount of a commission merchant's commission, how do you find the selling price? 10. If you know the price at which a commission merchant sells some goods, and the amount of his commission, how do you find the rate? 11. On what is an insurance premium reckoned? How is the rate stated? 12. If you know the face of an insurance policy, and the premium, how do you find the rate ? 13. If you know the premium on an insurance policy, and the rate, how do you find the face of the policy? 14. What is a tax table, and how would you prepare one on the basis of 12 mills on a dollar? 15. If you know the assessed valuation of a man's property, and the rate of taxation, how do you find his tax? 16. If you know the assessed valuation of a man's property, and his tax, how do you find the rate? 17. If you know the tax paid by a man, and the rate of taxation, how do you find the assessed valuation of his property? 18. If you know the amount of tax to be raised and the total assessed valuation, how do you find the tax rate? 19. If you know the number of units of some imported goods, and the rate of specific duty, how do you find the amount of the duty? 20. If you know the value of some imported goods, and the rate of duty ad valorem, how do you find the amount of duty? 21. Given the principal, rate, and time, how do you find the interest? 22. Given the principal, rate, and interest, how do you find the time? 23. Given the principal, interest, and time, how do you find the rate? 24. Given the rate, time, and interest, how do you find the principal? 25. How would you proceed to compute an interest table, given the rate? 26. If you have an example in partial payments, all the dates within a single year, how do you proceed to solve? 27. If you have an example in partial payments extending beyond a year, how do you proceed to solve? 28. How do you express a given per cent as a common fraction? 29. If you are to find a certain fractional part of a number, how do you express this as a per cent? 30. If you have a certain rate per cent expressed with the per cent sign, how do you express it as a decimal fraction? 31. If you have a decimal fraction and wish to express the same number with a per cent sign, how do you proceed? If you know what a given per cent of a number is, how do you find the number? 32. 33. How do you find what per cent one number is of another? Illustrate. 34. A man's salary two years ago was increased a certain per cent. Last year it was decreased the same per cent. Is his salary at present greater than or less than it was two years ago? 35. A merchant marks his goods a certain per cent above cost. Owing to hard times, he sells them at the same per cent below the marked price. Does he sell them for more than or less than cost? 36. Which is the greater, the common interest on a certain sum or the exact interest? Why is this? 37. What are the common methods of finding the difference between two given dates? Which one is the more exact? 38. State the easiest way of finding the interest on a given sum of money for sixty days at 6%. 39. How would you find the compound interest on a given sum of money for a certain number of years at a given rate? CHAPTER II RATIO AND PROPORTION 58. Ratio. The relative magnitude of two numbers, as expressed by the fraction which has the first number for the numerator and the second for the denominator, is called the ratio of the first number to the second. The ratio of 2 to 3, or 3, is commonly written 2 : 3. 59. Antecedent and Consequent. The first term of a ratio is called the antecedent, and the second term the consequent. 60. Ratios always Abstract. The two terms of a ratio always being like numbers, as in 2:3, $4: $5, 6 ft.: 7 ft., the quotient is always abstract. Therefore, a ratio is always abstract, and its terms may be written as abstract numbers. Instead of writing 2 ft. we may therefore write simply 3 It is better to use the fractional form at first, and then to use the other form, 2:3. 61. Reduction of Ratios. Since a ratio may be expressed as a fraction, therefore If the terms of a ratio are both multiplied by or both divided by the same number, the value of the ratio is not altered. Thus, if both terms of the ratio 21:31 are multiplied by 6, the resulting ratio is 15: 20, and these two ratios are equal. Again, since 15 = 3, the simplest expression for 21: 31 is 3: 4. 62. Separating a Number in a Given Ratio. Required to separate $63 in the ratio of 3 to 4. Since there must be $3 in the first part to every $4 in the second, there must be $7 every time two such amounts are taken out. Therefore the first part must contain of the total and the second 4. But of $63 is $27, and 4 of $63 is $36. These are the results, because $27: $36 Find the missing term in each of the following ratios: 28. Two farmers pay $15 together for some threshing, one having 350 bu. and the other 400 bu. of wheat. What is the share of each? 29. A man leaves an estate of $13,470, giving $1 to his widow for every $2 to his children. How much did the children receive? |