its taxable property is inventoried at $199500. What amount of tax must be raised to pay the debt and 5 per cent. commission for collection; and what is the tax on a dollar? Solution. The sum to be raised is $6000; (Art. 458;) and the tax is 3 cents on a dollar. (Art. 456.) Now, since the tax on $1 is $.03, it is obvious that multiplying $.03 by 2 will be the tax on $2; multiplying it by 3, will be the tax on $3, &c., as seen in the following 15. In the above assessment, what is A. B.'s tax, who is rated at $2256, and pays for 3 polls? Operation. $2000 pay $60.00 200 6.00 50 66 1.50 6 66 1.50 3 polls .18 $2256=2000+200+50+6 dollars. Now if we add together the tax paid on each of these sums, as found in the table above, the amount will be the tax on $2256. Amount, $69.18 A. B.'s tax therefore is $69.18. 16. What is G. A.'s tax, who is assessed for 2 polls, and $2400 ? 17. What is H. B.'s tax, who is assessed for 1 poll, and $3850? 18. What is W. C.'s tax, who is assessed for 3 polls, and $15000? 19. E. D. is assessed for $16024, and 1 poll: what is his tax? 20. J. F. is assessed for $10450, and 2 polls: what is his tax? 21. T. G. is assessed for $20680, and 3 polls: what is his tax? 22. W. H. is assessed for $17530, and 1 poll: what is his tax? 23. L. J. is assessed for $8760, and 1 poll: what is his tax? 24. W. L. is assessed for $21000, and 2 polls: what is his tax? 25. J. K. is assessed for $6530, and 2 polls: what is his tax? 26. G. L. is assessed for $13480, and 1 poll: what is his tax? 27. F. M. is assessed for $12300, and 3 polls: what is his tax? 28. C. P. is assessed for $15240, and 2 polls: what is his tax? 29. J. S. is assessed for $16000, and 1 poll: what is his tax? 30. R. W. is assessed for $18000, and 2 polls: what is his tax? Note.-Rate Bills for schools are generally apportioned according to the number of days each scholar has attended. Hence, 460. To make out Rate Bills for schools. First find the number of days attendance of all the scholars, and the whole amount of expenses, including teacher's salary, fuel, repairs, &c. From the amount of expenses deduct the public money, if any, then divide the remainder by the whole number of days attendance, and the quotient will be the rate per day. Finally, multiply the rate per day by the number of days attendance of each man's children, and the product will be his tax. OBS. In New York and some other states, the general principle is to include only the Teacher's Salary in the Rate Bill. (Revised Statutes. N. Y.) 31. A certain district paid $130 for teacher's salary, $34 for board, $19.42 for fuel, and $2.58 for repairs; the district drew $30 public money, and the whole number of days attendance was 2400: what was the rate per day; and how much was A's tax, who sent 115 days? Solution.-Amount of expenses, $186-$30-$156; and $156 ÷2400=$.065, the rate per day. Now $.065×115=$7.475, A's tax is therefore $7.475. 32. If the expenses of a district are $313.20, and the whole attendance 3915 days, what is B's tax, who sends 167 days? 33. A district paid their teacher $115, and their fuel cost $21.10; it drew $38.50 public money, and the number of days attendance was 1954: what was C's tax, who sent 69 days? 34. The expenses of a district were $215.20, and the number of days attendance 2150: what was D's tax, who sent 134 days? 298 ANALYSIS. [SECT. SECTION XIII. ANALYSIS. ART. 461. The term Analysis, in physical science, signifie resolving of a compound body into its elements, or component p ANALYSIS, in arithmetic, signifies the resolving of numbers the factors of which they are composed, and the tracing of relations which they bear to each other. (Art. 95. Obs. 2.) OBS. In the preceding sections the student has become acquainted with method of analyzing particular examples and combinations of numbers, thence deducing general principles and rules. But analysis may be app with advantage not only to the development of mathematical truths, but als the solution of a great variety of problems, both in arithmetic and pract life. Indeed, it is the method by which business men generally solve pr tical questions. A little practice will give the student great facility in application. 462. No specific directions can be given for solving exampl by analysis. None in fact are requisite. The judgment, fro the conditions of the question, will suggest the process. Henc Analysis may, with propriety, be called the COMMON SENSE RUL OBS. In solving questions analytically, it may be remarked in general, the we reason from the given number to 1, then from 1 to the number required. Ex. 1. If 60 yards of cloth cost $240, what will 85 yards cost Analytic solution.-Since 60 yds. cost $240, 1 yd. will cost of $240; and of $240 is $4. Now if 1 yd. costs $4, 85 yds. will cost 85 times as much; and $4X85=$340. Ans. Or, we may reason thus: 85 yds. are 5 of 60 yds.; therefore 85 yds. will cost 85 of $240, (the cost of 60 yds.) and 35 of $240 is $240X85 $340, the same as before. (Arts. 210, 212.) OBS. 1. Other solutions of this example might be given; but our present object is to show how this and similar questions may be solved by analysis. The QUEST.-461. What is meant by analysis in physical science? What in arithmetic ? To what may analysis be advantageously applied? 462. Can any particular rules be prescribed for solving questions by analysis? How then will you know how to proceed? Obs. What is the operation of solving questions by analysis called? former method is the simplest and most strictly analytic, though not so as the latter. It contains two steps: First, we separate the given price of 60 yds. ($240) into 60 equal par find the value of one part, or the cost of 1 yd., which is $4. Second, we multiply the price of 1 yd. ($4) by 85, the number of yds. w cost is required, and the product is the answer sought. 2. This and similar questions are usually placed under the rule of S Proportion, or the Rule of Three. 3. The operation of solving a question by analysis, is called an and solution. In reciting the following examples, each one should be anal and the reason for every step given in full. 2. A man bought a horse, and paid $45 down, which was the price of it: what did he give for the horse? Analysis. Since $45 is of the price, the question reso itself into this: $45 is of what sum? sum, is of $45; and of $45 is $9. If $45 is of a cer 7 sevenths are 7 times as much; and $9×7=$63. Ans. $6 PROOF. of $63=$9, and 5 sevenths are 5 times as m which is $45, the sum he paid down for the horse. Note. In solving examples of this kind, the learner is often perplex finding the value of , &c. This difficulty arises from supposing that of a certain number is 45, of it must be of 45. This mistake wi easily avoided by substituting in his mind the word parts for the giver nominator. Thus, if 5 parts cost $45, 1 part will cost of $45, which i But this part is a seventh. Now if 1 seventh cost $9, then 7 seventh cost 7 times as much. 3. If 40 cords of wood cost $120, how much will 100 c cost? 4. Bought 35 tons of hay for $700: how much will 16 cost? 5. What cost 37 gallons of molasses, at $21 a hogshead? 6. What cost 1500 pounds of hay, at $14 per ton? 7. What cost 18 quarts of chestnuts, at $3 a bushel? 8. If 55 tons of hemp cost $660, what will 220 tons cost at same rate? 9. If 165 bushels of apples cost $132, how much will 31 bus cost? 300 ANALYSIS. [SECT 10. It 72 bushe's of peanuts cost $253.44, what will cost at the same rate? 11. If 150 acres of land cost $7000, what will a squa cost? 12. If 2 pipes of wine cost $315, what is that per gill ? 13. A farmer bought a yoke of oxen, and paid $40 in which was of the cost: what did they cost? 14. Bought a house, and paid $630 in goods, which was the price of it: what was the cost of the house? 15. A young man lost $256 by gambling, which was he was worth: how much was he worth? 16. A man having $1500, paid 3 of it for 112 acres of how much did his land cost per acre? 17. If a stack of hay will keep 350 sheep 90 days, how will it keep 525 sheep? 18. If 440 bbls. of flour will last 15 men 55 months, how will the same quantity last 28 men ? 19. If 136 men can build a block of stores in 120 days, long will it take 15 men to build it? 20. If of a pound of tea cost 40 cents, what will of a po cost? 21. If of a yard of broadcloth cost $2.50, how much wi of a yard cost? 22. Bought of a ton of hay for $3.42: how much will a ton cost? 23. Bought of a hogshead of molasses for $38.19: h much will of a hogshead cost? 24. If of an acre of land cost $108, how much will of acre cost? 25. If of a barrel of beef cost $6.48, how much will of barrel cost? 26. Paid $4200 for of a sloop: how much can I afford sell of the sloop for? 27. Sold 18 baskets of peaches for $34: how much would 65 baskets come to? 28. If I pay $60.50 for building 20 rods of wall, how much must I pay for 215 rods? |