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Question 1172596:
2. Marie sells two types of alcohol. The green cross alcohol 500 ml that costs Php120 and the casino rubbing alcohol 150 ml which costs Php 45. She has to sell at most Php1000 per day for both sizes of alcohol. Find the inequality that represents the situation. (don't forget to graph)
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! **1. Define Variables**
* Let `x` be the number of Green Cross alcohol bottles sold.
* Let `y` be the number of Casino rubbing alcohol bottles sold.
**2. Set Up the Inequality**
* **Cost of Green Cross alcohol:** 120x
* **Cost of Casino rubbing alcohol:** 45y
* **Total sales:** 120x + 45y
* **Sales constraint:** 120x + 45y ≤ 1000
**3. Simplify the Inequality**
Divide the inequality by 3 to simplify:
40x + 15y ≤ 333.33 (approximately)
**4. Graphing the Inequality**
To graph this inequality, we'll follow these steps:
* **Find the intercepts:**
* **x-intercept:** Set y = 0 and solve for x: 40x ≤ 333.33 => x ≤ 8.33
* **y-intercept:** Set x = 0 and solve for y: 15y ≤ 333.33 => y ≤ 22.22
* **Plot the intercepts:**
* Plot the point (8.33, 0) on the x-axis.
* Plot the point (0, 22.22) on the y-axis.
* **Draw the boundary line:**
* Connect the intercepts with a solid line because the inequality includes the equal sign (≤).
* **Shade the solution region:**
* Since the inequality is "less than or equal to," shade the area below the line. This shaded region represents all the possible combinations of Green Cross and Casino alcohol bottles that Marie can sell to stay within her Php 1000 sales limit.
**Important Considerations**
* **Non-negative values:** Since Marie cannot sell a negative number of bottles, the solution region is restricted to the first quadrant (x ≥ 0, y ≥ 0).
* **Discrete values:** Marie can only sell whole bottles, so the solution should technically be a set of discrete points within the shaded region. However, for practical purposes, the continuous shaded region gives a good visual representation of the constraints.
**Let me know if you'd like a visual representation of the graph! I can describe it in more detail or provide a link to an online graphing tool where you can see the graph.**
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