Identifying Reasonable Solutions for a Situation Audrey has x pounds of red grapes and y pounds of green grapes. She has less than 5 pounds of grapes in all. Which are reasonable solutions for this situation? Check all that apply. (
, 2) (1, 3.5) (2, 2) (4.5, 0.5) (5, 0)
The Correct Answer and Explanation is:
To solve this problem, we are told:
Audrey has x pounds of red grapes and y pounds of green grapes. She has less than 5 pounds of grapes in all.
This means: x+y<5x + y < 5
We are given several ordered pairs (x, y), which represent the number of pounds of red and green grapes Audrey could have. We must check which combinations result in less than 5 pounds total.
Let’s evaluate each option:
- (0, 2):
0+2=20 + 2 = 2 → ✅ less than 5 - (1, 3.5):
1+3.5=4.51 + 3.5 = 4.5 → ✅ less than 5 - (2, 2):
2+2=42 + 2 = 4 → ✅ less than 5 - (4.5, 0.5):
4.5+0.5=54.5 + 0.5 = 5 → ❌ not less than 5 (it’s exactly 5) - (5, 0):
5+0=55 + 0 = 5 → ❌ not less than 5
✅ Correct answers:
- (0, 2)
- (1, 3.5)
- (2, 2)
Explanation (300 words):
This problem requires analyzing real-world constraints using inequality. Audrey has two types of grapes — red (x pounds) and green (y pounds) — and their total must be less than 5 pounds. Mathematically, this is expressed as: x+y<5x + y < 5
Each answer choice is a possible (x, y) pair. To determine if it’s reasonable, we calculate the total weight of grapes for each pair and check if the total is strictly less than 5. Note that exactly 5 pounds is not allowed; the total must be under 5 pounds.
Let’s analyze:
- (0, 2): Red = 0, Green = 2 → Total = 2 → This is valid.
- (1, 3.5): Red = 1, Green = 3.5 → Total = 4.5 → This is valid.
- (2, 2): Red = 2, Green = 2 → Total = 4 → This is valid.
- (4.5, 0.5): Red = 4.5, Green = 0.5 → Total = 5 → Not valid.
- (5, 0): Red = 5, Green = 0 → Total = 5 → Not valid.
Only the first three pairs satisfy the condition x + y < 5. This exercise helps build understanding of inequalities and how they relate to real-world limits. It’s also an example of how to apply mathematical reasoning when evaluating multiple options
.