# Equations and inequalities

You are planning on applying for a job with ABC Advertising. Many business decisions are based on unknown quantities, known as variables, encountered in business, economics, and social science. Thus, before the interview, you want to brush up on your knowledge of linear equations and linear inequalities. Complete the following. Be sure to show your work where applicable.

A. To increase your understanding, you first want to describe the differences between linear equations and linear inequalities.

B. Next, set up the following scenarios as equations or inequalities and then solve for the desired quantity:

1. Sales, given in thousands, for a particular company in 1990 were at 120.5 and in 2000 at 140.5, estimate the sales for the years 1997 and 2003. Let x = 0 correspond to 1990. Using the distance formula, find the approximate distance between the values in 1997 and 2003. Explain the difference between using the distance formula and simply subtracting the two estimated values.

2. To rent a car from the airport it will cost $25 per day plus $0.25 per mile traveled. How many miles could you travel in 1 day for at least $50 and no more than $100? What if you wanted to travel for 2 days with the same restrictions? How would the problem change and what would be the mileage?

3. A printing company charges $12.00 per order plus $0.15 per page for printing flyers. A second company charges $10.50 per order plus $0.25 per page. Find the equilibrium point and explain what this point means in the context of the data.

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1. Sales, given in thousands, for a particular company in 1990 were at 120.5 and in 2000 at 140.5, estimate the sales for the years 1997 and 2003. Let x = 0 correspond to 1990. Using the distance formula, find the approximate distance between the values in 1997 and 2003. Explain the difference between using the distance formula and simply subtracting the two estimated values.

First of all, we know x = 0 correspond to 1990. Therefore, x = 10 correspond to 2000. So based on the Cartesian coordinate system, you have two points (0, 120.5), and (10, 140.5). We must find the regression line. Here is how we find such line.

. Then, we can calculate the line as followed. . Suppose we want to find at 1997, then x = 7 (since 1997 - 1990 = 7). Plug 7 into the equation of the line we get . At 2003, we get x = 13 . Now, you have two points (7, 134.5) and (13, 146.5). The distance is, using the distance formula, . Supposed you just simply subtract the two estimated ...

#### Solution Summary

This provides examples of working with equations and inequalities to model situations.