Questions: Systems of Two-Variable Linear Inequalities: Mastery Test
2. Solve this system by the system of inequalities:
Which solution could be represented by this system of inequalities?
4x + 5y ≥ 180
x + y ≤ 40
A. The owner wants to sell at least 40 items of clothing. The store sells no more than 180 pounds of oranges in a day, and
neither item's daily sales will exceed 40.
B. On a math test, questions are worth 4 or 5 points each. The test has 40 questions, and a maximum score of 180 points.
C. At a pharmacy, pills of generic and brand name cost 4 and 5 respectively. The maximum number of pills sold per day is 40, and
the store wants to make at least 180 per day.
D. At a pharmacy, space is limited to 40 boxes of cotton balls and bandages. Cotton balls cost 4 and bandages 5, with a minimum sales revenue of 180.
O A
O B
O C
O D
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Transcript text: Systems of Two-Variable Linear Inequalities: Mastery Test
2. Solve this system by the system of inequalities:
Which solution could be represented by this system of inequalities?
4x + 5y ≥ 180
x + y ≤ 40
A. The owner wants to sell at least 40 items of clothing. The store sells no more than 180 pounds of oranges in a day, and
neither item's daily sales will exceed 40.
B. On a math test, questions are worth 4 or 5 points each. The test has 40 questions, and a maximum score of 180 points.
C. At a pharmacy, pills of generic and brand name cost $4 and $5 respectively. The maximum number of pills sold per day is 40, and
the store wants to make at least $180 per day.
D. At a pharmacy, space is limited to 40 boxes of cotton balls and bandages. Cotton balls cost $4 and bandages $5, with a minimum sales revenue of $180.
O A
O B
O C
O D
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Solution
Solution Steps
Step 1: Understanding the Inequalities
We are given the system of inequalities:
\(4x + 5y \geq 180\)
\(x + y \leq 40\)
Here, \(x\) and \(y\) represent quantities related to a specific scenario. The first inequality indicates a minimum requirement, while the second indicates a maximum limit.
Step 2: Evaluating the Scenarios
We need to evaluate each scenario to see which one fits the given inequalities:
Scenario A: Discusses selling clothing and oranges, which does not align with the inequalities.
Scenario B: Involves a math test with point values and a maximum score, which also does not fit.
Scenario C: Relates to a pharmacy selling pills at prices of $4 and $5, with a maximum of 40 pills and a minimum revenue of $180. This scenario aligns with the inequalities.
Scenario D: Involves cotton balls and bandages, which does not match the inequalities.
Step 3: Conclusion
After evaluating the scenarios, we find that Scenario C is the only one that satisfies both inequalities.