3b. Roger discovers that he needs to buy some chicken as well. He buys an amount of chicken that weighs more than the beef he bought and less than the turkey he bought.

Question

Which amount of chicken could Roger have bought?

Be sure to work out the problem on paper and use a calculator if needed.

(2 points)
Responses

2.75 pounds of chicken
2.75 pounds of chicken

3.2 pounds of chicken
3.2 pounds of chicken

3.7 pounds of chicken
3.7 pounds of chicken

4 pounds of chicken

GPT-4o mini · Answer

To determine the amount of chicken Roger could have bought, we need to establish the weights of the beef and turkey he purchased, and then find a weight for the chicken that is more than the weight of the beef and less than the weight of the turkey.

Let's summarize the conditions:

Beef: Represents a certain weight (let's call it \( B \))
Turkey: Represents a certain weight (we'll call it \( T \))
Chicken: Must weigh more than beef and less than turkey, so the conditions are: \[ B < C < T \]

We don't have specific weights for beef and turkey, which means we can't calculate specific values for C, the weight of chicken. However, we can analyze the options given based on the potential ranges of beef and turkey.

The options provided are:

2.75 pounds of chicken
3.2 pounds of chicken
3.7 pounds of chicken
4 pounds of chicken

To find a valid option for C, we would assume different possibilities for B and T in order to check which of the options could be valid.

Let's say:

If Roger's beef weight \( B \) was 2.5 pounds (as an example)
If his turkey weight \( T \) was 4 pounds

Then the valid range for chicken would be: \[ 2.5 < C < 4 \] In this situation, the valid chicken weights from the options would be:

2.75 pounds (valid)
3.2 pounds (valid)
3.7 pounds (valid)
4 pounds (not valid)

If we use another scenario:

If \( B \) was 3.5 pounds and \( T \) was 4.5 pounds

The valid range for chicken would be: \[ 3.5 < C < 4.5 \] In this scenario, the valid weights would be:

2.75 (not valid)
3.2 (valid)
3.7 (valid)
4 (valid)

Every exploration shows that some options fit the criteria of being more than B and less than T, but without specific weights for beef and turkey, we can’t definitively rule on one specific option.

To conclude and select a response based on the analysis, we could reasonably present multiple answers depending on variably set B and T. However, from the options provided, 3.2 pounds of chicken, 3.7 pounds of chicken, and 4 pounds of chicken are likely candidates, with 3.2 pounds being especially sensible since it’s a moderate choice that would likely fit many potential B and T ranges.

The final answer can lean towards:

3.2 pounds of chicken.