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Answer :
Sure! Let's analyze the inequality and understand the relationship between the pounds of apples (a) and the pounds of bananas (b) that Marcus needs to buy.
The given inequality is:
[tex]\[2a \leq b\][/tex]
To understand what this means, let's rearrange the inequality to isolate [tex]\(a\)[/tex]:
1. Divide both sides of the inequality by 2:
[tex]\[ a \leq \frac{b}{2} \][/tex]
This tells us that the number of pounds of apples ([tex]\(a\)[/tex]) that Marcus needs to buy must be less than or equal to half the number of pounds of bananas ([tex]\(b\)[/tex]) he needs to buy.
Now, let's interpret this in terms of the options provided:
1. Marcus needs to buy at least twice as many pounds of apples as pounds of bananas.
- This would imply [tex]\(a \geq 2b\)[/tex], which doesn't match our inequality.
2. Marcus needs to buy exactly as many pounds of apples as pounds of bananas.
- This would imply [tex]\(a = b\)[/tex], which doesn't match our inequality.
3. Marcus needs to buy at least twice as many pounds of bananas as pounds of apples.
- This would imply [tex]\(b \geq 2a\)[/tex], which matches our inequality. But note, "at least" might be misleading since we are looking for an exact nature from the options below.
4. Marcus needs to buy at most twice as many pounds of bananas as pounds of apples.
- This matches [tex]\(a \leq \frac{b}{2}\)[/tex] exactly as we have found above.
Therefore, the correct interpretation is:
Marcus needs to buy at most twice as many pounds of bananas as pounds of apples.
The given inequality is:
[tex]\[2a \leq b\][/tex]
To understand what this means, let's rearrange the inequality to isolate [tex]\(a\)[/tex]:
1. Divide both sides of the inequality by 2:
[tex]\[ a \leq \frac{b}{2} \][/tex]
This tells us that the number of pounds of apples ([tex]\(a\)[/tex]) that Marcus needs to buy must be less than or equal to half the number of pounds of bananas ([tex]\(b\)[/tex]) he needs to buy.
Now, let's interpret this in terms of the options provided:
1. Marcus needs to buy at least twice as many pounds of apples as pounds of bananas.
- This would imply [tex]\(a \geq 2b\)[/tex], which doesn't match our inequality.
2. Marcus needs to buy exactly as many pounds of apples as pounds of bananas.
- This would imply [tex]\(a = b\)[/tex], which doesn't match our inequality.
3. Marcus needs to buy at least twice as many pounds of bananas as pounds of apples.
- This would imply [tex]\(b \geq 2a\)[/tex], which matches our inequality. But note, "at least" might be misleading since we are looking for an exact nature from the options below.
4. Marcus needs to buy at most twice as many pounds of bananas as pounds of apples.
- This matches [tex]\(a \leq \frac{b}{2}\)[/tex] exactly as we have found above.
Therefore, the correct interpretation is:
Marcus needs to buy at most twice as many pounds of bananas as pounds of apples.
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