To determine which equivalent expressions are represented by the model set up by the farmer, let's analyze the expressions you provided based on the principles of algebra.
Given the setup, we can assume the model might be related to the distributive property and common factors.
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(5)(3) + (5)(1): This expression can be simplified to \(5 \times (3 + 1) = 5 \times 4\). So, it is equivalent.
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5(3+1): This is simply \(5 \times 4\) and is obviously equivalent to the other expressions.
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15 + 5: This simplifies to \(20\), which is not equivalent to \(5 \times (3 + 1)\) or \((5)(3) + (5)(1)\).
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3(5+1): This simplifies to \(3 \times 6 = 18\), which is not equivalent to the previous expressions.
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3 + (5 + 1): This simplifies to \(3 + 6 = 9\); It is not equivalent to the previous expressions.
Based on this reasoning, the three equivalent expressions are:
- (5)(3) + (5)(1)
- 5(3 + 1)
- (the third option does not work here, you would select any other option you can verify in the context)
From the choices given, the two you can certainly select as equivalent would be (5)(3) + (5)(1) and 5(3 + 1). Unfortunately, none of the other responses qualify as the third correct choice in this particular set.
Final Answers:
- (5)(3) + (5)(1)
- 5(3 + 1)
You may want to adjust your model or statements to include a third expression that is equivalent, as it currently lists more than select few, but in the provided choices, these two are confirmed equivalent.