Three football players from the Mustang junior football team each spent 20 minutes loading boxes of food onto a truck for a local charity. The number of boxes, b, that each player loaded onto the truck is proportional to the number of minutes, m, spent loading boxes.

Question

Alonzo loaded 14 boxes.
Bennett loaded one fourth as many boxes as Cory.
Cory loaded twice as many boxes as Alonzo.
Select all of the true statements.

The equation that represents the number of boxes Alonzo loaded is b = 0.7m.
The equation that represents the number of boxes Bennett loaded is b = 0.35m.
For each player, the proportional relationship b = rm can be used to determine the rate, r, at which each player loaded the boxes.
The equation that represents the number of boxes Cory loaded is b = 2m.
The proportional relationship can be used to determine the rate, r, at which the players loaded the boxes.
Based on the rates of loading boxes onto the truck, Alonzo and Bennett loaded boxes at the same rate.

Answer 1

Let's analyze the information given in the problem to determine the true statements:

1. Alonzo loaded 14 boxes.

   • He spent 20 minutes loading boxes.

   We can find his rate of loading boxes: \[ r_A = \frac{b_A}{m_A} = \frac{14 \text{ boxes}}{20 \text{ minutes}} = 0.7 \text{ boxes per minute} \] So the equation for Alonzo's loading would indeed be: \[ b = 0.7m \]

   True: The equation that represents the number of boxes Alonzo loaded is \( b = 0.7m \).

2. Cory loaded twice as many boxes as Alonzo.

   • Since Alonzo loaded 14 boxes, Cory loaded: \[ b_C = 2 \cdot 14 = 28 \text{ boxes} \]

   We can find Cory's rate of loading boxes: \[ r_C = \frac{b_C}{m_C} = \frac{28 \text{ boxes}}{20 \text{ minutes}} = 1.4 \text{ boxes per minute} \] Thus, Cory's equation would be: \[ b = 1.4m \]

   The statement suggests the equation: \[ b = 2m \] does not hold true as it does not correctly represent the rate based on time and boxes loaded.

   False: The equation that represents the number of boxes Cory loaded is \( b = 2m \).

3. Bennett loaded one fourth as many boxes as Cory.

   • Therefore, Bennett loaded: \[ b_B = \frac{1}{4} \cdot 28 = 7 \text{ boxes} \]

   Finding Bennett's rate of loading boxes: \[ r_B = \frac{b_B}{m_B} = \frac{7 \text{ boxes}}{20 \text{ minutes}} = 0.35 \text{ boxes per minute} \]

   Thus, his equation would be: \[ b = 0.35m \]

   True: The equation that represents the number of boxes Bennett loaded is \( b = 0.35m \).

4. For each player, the proportional relationship \( b = rm \) can be used to determine the rate, r, at which each player loaded the boxes.

   This relationship is valid since it's common to express proportional relationships this way, where \( r \) would be the boxes per minute for each player:

   • Alonzo: \( r_A = 0.7 \)
   • Bennett: \( r_B = 0.35 \)
   • Cory: \( r_C = 1.4 \)

   True: For each player, the proportional relationship \( b = rm \) can be used to determine the rate, r, at which each player loaded the boxes.

5. The proportional relationship can be used to determine the rate, r, at which the players loaded the boxes.

   Similar to the previous statement, since we can calculate the rates from the proportional relationships:

   True: The proportional relationship can be used to determine the rate, r, at which the players loaded the boxes.

6. Based on the rates of loading boxes onto the truck, Alonzo and Bennett loaded boxes at the same rate.

   From our calculations:

   • Alonzo’s rate: \( 0.7 \text{ boxes per minute} \)
   • Bennett’s rate: \( 0.35 \text{ boxes per minute} \)

   They loaded at different rates.

   False: Based on the rates of loading boxes onto the truck, Alonzo and Bennett loaded boxes at the same rate.

Summary of True Statements:

• The equation that represents the number of boxes Alonzo loaded is \( b = 0.7m \).
• The equation that represents the number of boxes Bennett loaded is \( b = 0.35m \).
• For each player, the proportional relationship \( b = rm \) can be used to determine the rate, r, at which each player loaded the boxes.
• The proportional relationship can be used to determine the rate, r, at which the players loaded the boxes.

Answer 2

what's the answer

Answer 3

Based on the analysis provided, the true statements are:

1. The equation that represents the number of boxes Alonzo loaded is \( b = 0.7m \).
2. The equation that represents the number of boxes Bennett loaded is \( b = 0.35m \).
3. For each player, the proportional relationship \( b = rm \) can be used to determine the rate, r, at which each player loaded the boxes.
4. The proportional relationship can be used to determine the rate, r, at which the players loaded the boxes.

The false statements are:

1. The equation that represents the number of boxes Cory loaded is \( b = 2m \) (this is false; the correct relationship is \( b = 1.4m \)).
2. Based on the rates of loading boxes onto the truck, Alonzo and Bennett loaded boxes at the same rate (this is false; Alonzo loaded at a higher rate of 0.7 boxes per minute compared to Bennett's 0.35 boxes per minute).

So, the final answers are the four true statements listed above.