Expressions

Buying a Home

For most people, buying a house is a great investment that can offer security in an uncertain world, but buying a house is also a commitment.

Application Practice

Answer the following questions. Use Equation Editor to write mathematical expressions and equations. First, save this file to your hard drive by selecting Save As from the File menu. Click the white space below each question to maintain proper formatting.

1. Imagine you are in the market for a new home and are interested in a new housing community under construction in a different city.
a. The sales representative informs you that there are 56 houses for sale with two floor plans still available. Use x to represent floor plan one and y to represent floor plan two. Write an equation that illustrates the situation.

b. The sales representative later indicates that there are three times as many homes available with the second floor plan than the first. Write an equation that illustrates this situation. Use the same variables you used in Part a.

c. Use the equations from Parts a. and b. of this exercise as a system of equations. Use substitution to determine how many of each type of floor plan is available. Describe the steps you used to solve the problem.

d. What are the intercepts of the equation from Part a. of this problem? What are the intercepts from Part b. of this problem? Where would the lines intersect if you solved the system by graphing?

2. As you are leaving the community, you notice another new community just down the street. Because you are in the area, you decide to inquire about it.

a. The sales representative here tells you they also have two floor plans available, but they only have 38 homes still for sale. Write an equation that illustrates the situation. Use x and y to denote floor plan one and floor plan two respectively.

b. The representative tells you that floor plan one sells for $175,000 and floor plan two sells for $200,000. She also mentions that all the available houses combined are worth $7,200,000. Write an equation that illustrates this situation. Use the same variables you used in Part a.

c. Use elimination to determine how many houses are available in each floor plan. Explain how you arrived at your answer.

3. You recently started the paperwork to purchase your new home, and were just notified that you can move into the house in 2 weeks. You decide to hire a moving company, but are unsure which company to choose. You search online and are interested in contacting two companies, Heavy Lifting and Quick Move, to discuss their rates. Heavy Lifting charges an $80 fee plus $35 per hour. Quick Move charges $55 per hour with no additional fees.

a. Which mover provides a better deal for 2 hours of work? How did you arrive at your answer?

b. Which mover provides a better deal for 15 hours of work? How did you arrive at your answer?

c. For what values h (hours) does Quick Move offer the better deal? Express your answer as an inequality. Explain how you reached your answer.