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# Real Life Scenarios: Systems of Linear Equations

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Determine a simple real-life example scenario to solve systems of linear equations

- Discuss how the math concept applies to your scenario. Scenarios or examples should clearly demonstrate how the math principle can be used to solve a real-life problem.

- Research and include references formatted consistent with APA guidelines if necessary.

Submit a 1-paragraph summary of each of your discussed example scenarios and math principles.

- Include any necessary variables, clearly defined.
- Include any formulas necessary to solve this problem.
- Include written descriptions of your logic, as needed, to explain the transition from words to mathematics.
- Solve the problem by demonstrating and explaining the step-by-step work involved to reach the answer.

https://brainmass.com/math/linear-transformation/real-life-scenarios-systems-linear-equations-552043

#### Solution Preview

Mike Brown plans to get a cell phone. There are two phone companies he can select from. Rogers charges a \$50 flat fee plus \$0.02 per minute, while Bell charges a \$20 flat fee plus \$0.04 per minute. If Mike thinks he may phone about 600 minutes a month, which phone company should he ...

#### Solution Summary

The solution discusses real life scenario based on systems of linear equations.

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## Solve linear equations and compounding interest

Among the professionals you have interviewed for your article, were several state and federal government spokespersons who use linear equations in a variety of ways.

An employee of the National Parks Service told you about a location in Washington, DC. It is a large grassy area south of the White House known as the Ellipse. The National Tree Lighting Ceremony is held annually on the Ellipse. Because the President officiates at this event, the Secret Service makes calculations which they use in planning security.

The Ellipse is actually an ellipse with major axis of length 1048 ft. and minor axis of length 898 ft. Assuming that a coordinate system is superimposed on the area in such a way that the center is at the origin and the major and minor axes are on the x- and y- axes of the coordinate system, respectively, find an equation of the ellipse.

The Board of Governors at the Federal Reserve Bank set the prime interest rate. These rates trickle down through the economy at various rates and affect consumer spending and saving habits. The economists at the Federal Reserve follow sample households in order to extrapolate information which they use in forecasting. For example, in one household they studied, the family made an investment for 1 year that earned \$7.50 simple interest. If the principal had been \$25 more and the interest rate 1% less, the interest would have been the same. Find the principal and the rate.

Another family in the Federal Reserve study group borrowed \$120,000. The loan is to be repaid in 13 years at 12% interest, compounded annually. How much will be repaid at the end of 13 years?

Twice a week, the State of Michigan runs a 6 out of 49 number lotto that pays at least \$2 million. The State needs to know the probabilities of winning in order to ensure that the lottery has ample reserves for the payouts. You purchase a card for \$1 and pick any 6 numbers from 1 to 49. If your numbers match those that the state draws, you win. How many 6-number combinations are there for the drawing? If you buy one ticket, what is your probability of winning (6 out of 6)?

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