# College Math 116 Week 8 Answer Guide- Algebra 1A -

### Week Eight Algebra 1A study guide and Soultions

#### 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.

*x *+ *y *= 56

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.

*y *= 3*x*

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.

Substitute 3*x *for the *y *in the first equation. Doing this leaves 4*x*=56, so *x*=14. Then, substitute 14 for *x *in either equation to find that *y*=42. This means there are 14 homes with floor plan one and 42 homes with floor plan two.

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?

For the first equation, the intercepts are (56, 0) and (0,56). The intercept for the second equation is (0, 0). The lines would intersect at (14, 42).

#### 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.

*x *+ *y *= 38

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.

175,000*x *+ 200,000*y *= 7,200,000

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

Answer by either multiplying the first equation by -175,000 or -200,000. This eliminates one variable. You can then solve for the remaining variable and substitute it into the first equation to find the second variable. You must arrive at the answer (16, 22). This means there are 16 available houses with floor plan one, and 22 available houses with floor plan two.

#### 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?

Heavy Lifting would charge $150 for 2 hours and Quick Move would charge $110. For 2 hours of work, Quick Move would be the better company. To find the fee for Heavy Lifting, multiply the number of hours by the hourly rate and add the fee. To find the fee for Quick Move, multiply the number of hours by the hourly rate.

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

For 15 hours of work, Heavy Lifting would charge $605 and Quick Move would charge $825. In this case, Heavy Lifting would be the better company.

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.

You can use the method of guess and check or set up a system of equations. Quick Move offers the better deal for less than 4 hours. 0 < *h *< 4 . When *h *= 4 , both companies offer the same deal. Neither is better.