# Word Problems Involving Linear Equations in Two Variables

1. Suppose 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 two floor plans still available, and that there are a total of 56 houses available. Use x to represent floor plan #1 and y to represent floor plan #2. Write an equation that illustrates the situation.

b) The sales representative later indicates that there are 3 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 part 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 available. Write an equation that illustrates the situation. Use x and y to denote floor plan #1 and floor plan #2 respectively.

b) The representative tells you that floor plan #1 sells for $175,000 and floor plan #2 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 with each floor plan are available. Explain how you arrived at your answer.

3. You recently started the paperwork to purchase your new home, and you 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 Lifters 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.

(See attachments for Word documents containing the above questions)

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#### Solution Summary

The solution is given as an attachment which contains 3 pages, one for each question, with equations written in Mathtype. Full step by step solutions are given with explanation.

The questions all involve converting word problems into equivalent linear equations in two variables, and then solving using substitution and elimination. These questions are typical of the sort asked in introductory College and High School algebra classes.

Algebra: Solving equations, graphing, inequalities, word problems.

15. A mathematics instructor asked her students to keep track of how much time each spent studying the chapter on percent notation in her basic mathematics course. She collected the information, together with test scores from that chapter's test, in the table below.

a). Use the two points reporting data for 9 hours of study time and 23 hours of study time and find a linear function that fits the data. (You can ignore the other lines of data in the chart.)

b.) Use the function to predict the test score of someone who has studied for 18 hours.

Study Time, x (in hours) Test Grade, y (in percent)

9 74

11 94

13 81

15 86

16 87

17 81

21 87

23 92

16. Define your variable and write an equation that could be used to solve the following problem. Do not solve the equation.

Josh left a 15% tip for a meal. The total cost of the meal, including the tip, was $30.50. What was the cost of the meal before the tip was added?

17. Define your variable and write an equation that could be used to solve the following problem. Do not solve the equation.

The product of two consecutive odd integers is 255. Find the integers.

18. Define your variables and write a system of equations that could be used to solve the following problem. Do not solve the equations.

Madeline goes to a bank and gets change for a $50 bill consisting of all $5 bills and $1 bills. There are 22 bills in all. How many of each kind are there?

19. Solve 3(r - 6) + 2 > 4(r + 2) - 21 and express the solution as a graph, using solution set notation, and using interval notation.

20. Graph 2x + 3y ≥ 6.

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