Question

choose the tape diagram and equation that best represent the situation.
first tape diagram: total 52, divided into three x segments and one 7 segment.
second tape diagram: total 52, divided into seven (x+3) segments.
third tape diagram: total 52, divided into seven x segments and one 3 segment.

Explanation:

Step1: Analyze the third tape diagram

The third tape diagram has 7 sections of \( x \) and one section of 3, summing to 52. So the equation is \( 7x + 3 = 52 \). Let's check the first diagram: \( 3x + 7 = 52 \) (3 \( x \)s and a 7), second: \( 7(x + 3)=52 \) (7 \( x + 3 \)s). The third's structure (7 \( x \)s and a 3) matches \( 7x + 3 = 52 \), which is a valid representation.

Step2: Confirm the equation for the third diagram

Count the number of \( x \) segments (7) and the constant (3), total is 52. So the equation is \( 7x + 3 = 52 \), and the tape diagram is the third one (the bottom - most, blue - bordered) as it has 7 \( x \) parts and a 3 part, summing to 52.

Answer:

The tape diagram is the third (bottom - most) one, and the equation is \( 7x + 3 = 52 \).