**Problem Solving**

**Getting Started**

In this discussion, you will use problem-solving skills to solve a problem based on the first letter of your last name. Review the problem-solving resources below. Understanding how to approach problems using these techniques will help you solve many types of problems.

**Upon successful completion of the course material, you will be able to:**

- Communicate quantitative problems and their solutions clearly and correctly in written or oral form.
- Utilize critical thinking skills to evaluate quantitative information in everyday life.
- Formulate a plan based on the mathematical concepts that apply to a problem.
- Analyze the mathematical relationships and patterns that confront the modern world.

**Background Information**

**First** letter of your **Last **name

**Solve the problem**

Show and explain the steps you take to solve the problem; post your work and the solution.

A – D

A toll collector on a highway receives $3 for cars and $4 for buses. At the end of a 1-hour period, she collected $60. How many cars and buses passed through the toll booth during that period? List all possible solutions.

E – K

Two cars, 360 kilometers apart, begin driving toward each other on a long, straight highway. One car travels 80 km per hour and the other 100 km per hour. At the same time, a canary, starting on one car, flies back and forth between two cars as they approach each other. If the canary flies 120 km per hour and spends no time to turn around at each car, how far has it flown when the cars collide?

L – R

Suppose you are designing a rectangular garden and you have 22 meters of fencing with which to enclose the garden. Explain how a garden 7 meters long and 4 meters wide can be enclosed with the available fencing. What is the area of a garden with these dimensions? Using the 22 meters of fencing, what dimensions would provide the largest area for a garden?

S – Z

Consider the case in which each of two piles initially contains fifteen marbles, where one pile contains fifteen white marbles and the other pile contains fifteen black marbles. Suppose that on the first transfer, three black marbles are moved to the white pile. On the second transfer, any three marbles are taken from the white pile and put into the black pile. Demonstrate, with diagrams and words that you will always end up with as many white marbles in the black pile as black marbles in the white pile. List all possible solutions.

**Instructions**

- Review the rubric to make sure you understand the criteria for earning your grade.
- Make sure to read the following on Problem Solving:
- Review the rubric to make sure you understand the criteria for earning your grade.
- In the
**1.2 Discussion**forum respond by solving one of the problems above based upon the**First**letter of your**Last**name (W). You must show your work, not just give the answers. - Your initial posting needs to thoroughly answer the discussion question, using critical thinking and thoughtful reasoning.
- Your initial post is due by the end of the fourth day of the workshop.
- For your second post, choose one of your classmates’ initial posts and respond by stating whether you agree or disagree with their explanation and solution(s) and why.
- For your third post, choose one of the following tasks:
- Respond to a classmate who reviewed your post. The response should show evidence of critical thinking and quantitative reasoning.
- Choose another classmate’s initial post and respond by stating whether you agree or disagree with their explanation and solution(s) and why.

- Read and respond as well to any follow-up instructor questions directed to you, by the end of the workshop.
- Your postings should also:
- Be well developed by providing clear answers with evidence of critical thinking.
- Add greater depth to the discussion by introducing new ideas.
- Provide clarification to classmates’ questions and provide insight into the discussion.
- A response of ‘Good job,’ or a similar comment is not acceptable.
- Your two follow-up responses need to be clearly collaborative by taking the initiative to respond to classmates’ questions, providing clarification and insight on issues in the discussion.

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