# Word Problems

1. Find the quotient of 10 and 2 added to the product of 20 and 2.

2. The formula N=0.07x + 4.1 models the number of women, N, in millions, enrolled in U.S. colleges x years after 1984. How many years after 1984 is the projected enrollment for women expected to reach 6.2 million? In which year is this expected?

3.The optimum heart rate that a person should achieve during exercise for the exercise to be most beneficial is modeled by r =0.6(220-a), where a represents a person's age and r represents that person's optimum heart rate, in beats per minute. If the optimum heart rate is 120 beats per minute, how old is that person?

4. Describe the number line graph of the following inequality: x ≤-3

5. The length of a rectangular parking lot is 10 yards less than twice its width. If the perimeter of the lot is 400 yards, what are its dimensions?

6. To pass a course, you must have a final average of at least 60%. If a student scores 42 and 74 on the first two tests, what must be earned on the third test to pass the course?

7. A rectangular field is three times as long as it is wide. If the perimeter of the field is 400 yards, what are the field's dimensions?

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#### Solution Preview

1. Quotient of 10 and 2 = 10/2 = 5

Product of 20 and 2 = 20 x 2 = 40

Quotient of 10 and 2 added to the product of 20 and 2= 40+5=45

2. N=0.07x + 4.1 (N in millions)

N = 6.2

x = (6.2-4.1)/0.07 = 30

Hence, 30 years after 1984 the projected enrollment for women is expected to reach 6.2 million. In the year 2014, (1984+30), this is expected.

3. r =0.6(220-a), where a represents a person's age and r represents that person's optimum heart rate (in beats per minute).

r = 120

Therefore, 120 = 0.6(220-a)

Or, 220-a= 120/0.6 = ...

#### Solution Summary

This solution is comprised of detailed step-by-step calculations and explanation of the given problems and provides students with a clear perspective of the underlying concepts.

XYZ Advertising: Linear Regression Problem

Great news! XYZ Advertising has called you in for an interview to join its advertising team. During the interview process, you are expected to solve a linear regression problem. Consider the following data in the table below that show the cost for a Super Bowl ad from the years 1990-2006 and the average number of homes and viewers of the game.

Based on the data in the attached document, please supply the following:

1) Provide graphs of Cost versus Year, Average Number of Homes versus Year, and Average Number of Viewers versus Year.

2) Which pair from the first part has the best linear graph for predicting? Explain.

3) Create prediction equations for all three graphs, and explain what these equations mean.

4) Complete a 5-year prediction for advertising costs. Next, complete a 20-year prediction. Explain the validity in these predictions.

5) In what year would you expect the average number of viewers to reach 100 million? In what year would you expect the average number of homes to reach 50 million? Explain the validity of these predictions.

Objective: Use the Cartesian coordinate system to find the distance between two points; illustrate linear functions and their relationship to business, economics, social science, etc., and find the intersection of two lines.

A file for is attached for reference.

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