Two-Variable Linear Inequalities Answers
Select all of the following ordered pairs that are solutions to the inequality.
Ezra works two summer jobs to save for a laptop that costs at least $1100. He charges $15/hr to mow lawns and $10/hr to walk dogs. Recall the inequality that represents this situation: .Is (60, 20) a solution? How do you know? What does this point represent?
Yes, (60, 20) is a solution. When you substitute the values into the inequality, 15(60) + 10(20) ≥ 1100 becomes 900 + 200 ≥ 1100, or 1100 ≥ 1100. Since this is a true statement, the point is a solution. This point represents Ezra working 60 hours mowing lawns and 20 hours walking dogs, which earns him exactly the $1,100 he needs for the laptop.
Which of the following did you include in your solution?
Ezra works two summer jobs to save for a laptop that costs at least $1100. He charges $15/hr to mow lawns and $10/hr to walk dogs. Recall the inequality that represents this situation: Explain how to graph the solution set.
Graph the solid boundary line 15x + 10y = 1100 through (1100/15, 0) and (0, 110). Shade the region on or above the line in the first quadrant, where 15x + 10y ≥ 1100.
Which of the following did you include in your solution?
=✔ ><=
To see how the solution set changes, suppose the coordinate pair (a, b) satisfies the original inequality. If a stays the same, b must be less thanequal to✔ greater than its previous value to satisfy the new inequality.
Now suppose b stays the same. Then, a must be less thanequal to✔ greater than its previous value to satisfy the new inequality.
How is the graph of the solution affected?
.
60
Ezra works two summer jobs to save for a laptop that costs at least $1100. He considers adjusting his rates to the following:Lawn care: $250 per lawn for the summerDog walking: $300 per dog for the summerWhich inequality represents this situation?
If Ezra limits himself to 1 dog, how many lawns does he have to care for to reach his goal?
What is a solution to the inequality?
Ezra works two summer jobs to save for a laptop that costs at least $1100. He decides to adjust his rates to $250 per lawn (x) for the summer and $300 per dog (y) for the summer, and to limit himself to 2 dogs.Describe how to find a solution graphically.
First, write the inequality 250x + 300y ≥ 1100 and graph the boundary line in the first quadrant, since the number of lawns and dogs must be non-negative. Because the laptop costs at least $1100, shade the half-plane above the line (the side that does not include the origin). Then, draw a horizontal line at y = 2 to represent the limit of 2 dogs. The solutions are the points with integer coordinates that fall within the intersection of the shaded region and the area on or below the line y = 2.
Which of the following did you include in your answer?
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