# College Math 116 Week 4 Answer Guide- Algebra 1A -

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

#### 1. You are planning to spend no less than $6,000 and no more than $10,000 on your landscaping project.

a. Write an inequality that demonstrates how much money you are willing to spend on the project.

$6,000 £ *x *£ $10,000

b. For the first phase of the project, imagine you want to cover the backyard with decorative rock and plant some trees. You need 30 tons of rock to cover the area. If each ton costs $60 and each tree is $84, what is the maximum number of trees you can buy with a budget of $2,500? Write an inequality that illustrates the problem and solve. Express your answer as an inequality and explain how you arrived at your answer.

*t *£ 8

To solve this problem, multiply 60 by 30. This answer indicates how much the rock will cost, which is $1,800. Subtract $1,800 from $2,500 to arrive at $700. This means you have $700 to spend on trees. Divide $700 by the cost of each tree, which is $84. The answer, 8.3333…, indicates how many trees you can buy. Since you cannot buy a portion of a tree and do not have enough money to buy 9 trees, you can purchase a maximum of 8 trees.

c. Would five trees be a solution to the inequality in Part b? Justify your answer.

Yes. The number 5 is less than or equal to 8. The cost of 5 trees is also less than the cost of 8, so you are still under budget.

#### 2. The coordinate graph of the backyard shows the location of the trees, plants, patio, and utility lines. If necessary, you may copy and paste the image to another document and enlarge it.

a. What are the coordinates of Tree A, Plant B, Plant C, Patio D, Plant E, and Plant F?

Tree A (-20,20); Plant B (-20,-4); Plant C (-10, -14); Patio D (12,12), Plant E (8,-8); Plant F (18, -12)

b. The water line is given by the equation

12

3

2 *y *= - *x *-

Imagine you want to put a pink flamingo lawn ornament in your backyard. You want to avoid placing it directly over the water line in case you need to excavate the line for repairs in the future. Could you place it at point (-4, -10)?

Yes, it would not lie directly on the line, but it would be close to the water line. Some may argue that this may not be the best choice for the ornament, but they should determine that (-4, -10) is not a solution.

c. What is the slope and *y*-intercept of the line in Part b? How do you know?

12

3 2

= -

= -

*b*

*m*

The slope is the rate of change; It indicates how much the *y *will increase as *x *increases. The intercept *b *indicates the value of the line when *x *= 0.

d. Imagine you want to add a sprinkler system and the location of one section of the sprinkler line can be described by the equation

4 2

*y *= - 1 *x *-

Complete the table for this equation.

x y (x,y)

-6 -1 (-6, -1)

-2 -3 (-2, -3)

0 -4 (0, -4)

2 -5 (2, -5)

8 -8 (8, -8)

e. What objects might be in the way as you lay the pipe for the sprinkler?

Plant E lies on the line and will be an obstacle. Plant F, while not a solution, is close enough to the line that it may be a problem.