 Algebra - solving proportions - 2-3 pg paper needed

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Mathematics

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Solving Proportions

Assignment problems.pdf   Problems on this attachment

Read the following instructions to complete this assignment:

1. Solve problem 56 on page 437 of Elementary and Intermediate Algebra. Set up the two ratios and write your equation, choosing an appropriate variable for the bear population.
2. Complete problem 10 on page 444 of Elementary and Intermediate Algebra.
3. Write a two- to three-page paper (not including the title page) that is formatted in APA style and according to the Math Writing Guide. Format your math work as shown in the example, and be concise in your reasoning. In the body of your essay, do the following
• Set up the proportion for problem 56 on page 437.
• Demonstrate your solutions to problem 56 on page 437 and to problem 10 on page 444, making sure to include all mathematical work and an explanation for each step.
• Identify the form of equation you end up with in problem 10, and explain the relationship between the final coefficient of x compared to the original problem.
• Incorporate the following four math vocabulary words into your paper. Use bold font to emphasize the words in your writing. (Do not write definitions for the words; use them appropriately in sentences describing your math work.)
• Extraneous
• Proportion
• Cross multiply
• Extreme-means
MAT222.W1.AssignmentExample.pdf

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Running head: SOLVING PROPROTIONS 1 Running header should use a shortened version of the title if the title is long. Page number is located at right margin. (full title; centered horizontally & vertically) Solving Proportions John Q. Student MAT 222 Week 1 Assignment Instructor’s Name Date SOLVING PROPORTIONS 2 Solving Proportions (title required on first line) Proportions exist in many real-world applications, such as finding unit price or estimating an animal population. By comparing data from at least two experiments, conservationists are able to predict patterns of animal increase or decrease. In this situation, 300 bluegill in Spearhead Lake were tagged and released to estimate the size of the bluegill population. A month later, after capturing 120 bluegill from the same lake, proportions were used to determine the lake’s population. This new bluegill scenario can be solved by applying the same concept of proportions used in the “Capture-Recapture” method in #55 on page 437 (Dugolpolski, 2012). The concept of proportions allows the assumption the ratio of originally tagged fish to the whole population is equal to the ratio of recaptured tagged fish to the size of the sample. To determine the estimated solution, variables will be defined and rules for solving proportions used. The ratio of originally tagged bluegill to the whole population is 300 /x. The ratio of recaptured tagged bluegill to the sample size is 45/120. 300 = 45 This is the proportion set up and ready to solve. Cross multiplication is required X 120 at this point. The extremes are 120 and 300. The means are x and 45. 120(300) = 45x 36000 = 45x Divide both sides by 45. 45 45 x = 800 The bluegill population of Spearhead Lake is estimated to be around 800 fish. For the second problem in this assignment, the equation must be solved for y. Continuing the discussion of proportions, a single fraction (ratio) exists on both sides of the equal sign so basically it is a proportion, which can be solved by cross multiplying the extremes and means. y + 5 = -1 x-2 2 2(y + 5) = -1(x – 2) The result of the cross multiplying. SOLVING PROPORTIONS 3 2y + 10 = -x + 2 Distribute 2 on the left and -1 on the right. 2y + 10 – 10 = -x + 2 – 10 Subtract 10 from both sides. 2y = -x – 8 2y = -x – 8 Divide both sides by 2 2 2 y = -½ x - 4 This is a linear equation in the form of y = mx + b. After comparing the solution to the original problem, it is noticed that the slope, -½ ,is the same number on the right side of the equation. This indicates another method exists for solving the equation. y + 5 = -1 x-2 2 y + 5 = -1/2 (x-2) I would multiply both sides of the equation by (x – 2), which cancels the y+ 5 -5= -1/2x + 1 -5 denominator on the left, subtract 5 from both sides to get y alone, and y = -12/x -4 then simplify the right side. It would save a couple of steps from solving it the other way. Conclusion paragraph would go here. Remember to include 4-5 sentences to make a complete paragraph. SOLVING PROPORTIONS 4 Reference Dugopolski, M. (2012). Elementary and intermediate algebra (4th ed.). New York, NY: McGraw-Hill Publishing. Use the word ‘Reference’ or ‘References’ as the title. Text should ALWAYS be included in every assignment! Be sure to use appropriate indentation (hanging), font (Arial or Times New Roman), and size (12).
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