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Question

An illustration shows a set of three adjacent boxes labeled as Birds. Another set of four adjacent rectangles is labeled as Dogs and placed below Birds. All rectangles have the same dimensions. A bracket on the right side encompasses both sets and points to the number 42.

What is the value of one of the rectangles shown in the tape diagram?

(1 point)
Responses

1
1

7
7

14
14

6
6
Remaining Attempts : 3
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Answer 1

To deduce the value of one of the rectangles in the tape diagram, we need to interpret the information provided.

The brackets point to the total of 42, which encompasses both the Birds and the Dogs. The Birds set consists of 3 boxes, and the Dogs set consists of 4 rectangles.

Let's denote the value of each box in the Birds set as \( B \) and each rectangle in the Dogs set as \( D \).

From the information provided:

1. The total value from the Birds is \( 3B \).
2. The total value from the Dogs is \( 4D \).
3. Therefore, the equation representing the overall total is: \[ 3B + 4D = 42 \]

To find a solution, we could test out the given possible values for \( D \):

1. If \( D = 1 \): \[ 3B + 4(1) = 42 \Rightarrow 3B + 4 = 42 \Rightarrow 3B = 38 \Rightarrow B = \frac{38}{3} \quad \text{(not an integer)} \]

2. If \( D = 6 \): \[ 3B + 4(6) = 42 \Rightarrow 3B + 24 = 42 \Rightarrow 3B = 18 \Rightarrow B = 6 \quad \text{(integer)} \]

3. If \( D = 7 \): \[ 3B + 4(7) = 42 \Rightarrow 3B + 28 = 42 \Rightarrow 3B = 14 \Rightarrow B = \frac{14}{3} \quad \text{(not an integer)} \]

4. If \( D = 14 \): \[ 3B + 4(14) = 42 \Rightarrow 3B + 56 = 42 \Rightarrow 3B = -14 \quad \text{(not possible)} \]

The only integer solution we found is when \( D = 6 \), which led us to \( B = 6 \) as well.

Thus, the value of one of the rectangles (Dogs) is 6.

The answer is:

6