Ask a New Question
Menu

Use the image to answer the 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 - no response given

7
7 - no response given

14
14 - no response given

6
6 - correct
Correct.

Remaining Attempts : 2
Skip to navigation

1 answer

To find the value of one rectangle in the tape diagram, we can break down the information given:

  1. The three boxes labeled as Birds likely represent a total value associated with Birds.
  2. The four rectangles labeled as Dogs represent a total value associated with Dogs.

Together, these two sets add up to the number 42, as indicated by the bracket.

To find the value of one rectangle, we can segregate the total value among these sets. The simplest assumption is that the total value is related directly to the number of represented units.

Let’s assume:

  • The combined value of the Birds portion is \( B \).
  • The combined value of the Dogs portion is \( D \).

From the information: \[ B + D = 42 \]

If we denote each rectangle (whether it's a bird or dog) has the same value \( x \), then:

  • The value for Birds is \( 3x \) (from the three boxes labeled Birds).
  • The value for Dogs is \( 4x \) (from the four rectangles labeled Dogs).

Thus, we set up the equation: \[ 3x + 4x = 42 \]

This simplifies to: \[ 7x = 42 \]

To find \( x \): \[ x = \frac{42}{7} \] \[ x = 6 \]

Therefore, the value of one of the rectangles shown in the tape diagram is \( 6 \).