Which of the following equations represents the relationship where three times the width of a rectangle plus five is equal to seven more than four times the width?

To determine the correct equation representing the given relationship, let's break down the components of the statement.

The problem states that "three times the width of a rectangle plus five" can be expressed mathematically as 3w + 5, where w represents the width. The phrase "is equal to" indicates that we will create an equation. On the other side of the equation, we are told this expression "is equal to seven more than four times the width." The phrase "four times the width" translates to 4w, and "seven more than that" means we add 7, resulting in 4w + 7.

Putting the two parts together, we have 3w + 5 on one side and 4w + 7 on the other side, leading to the equation:

3w + 5 = 4w + 7.

This matches perfectly with option B, confirming that it accurately represents the described relationship. The structure of the equation is critical: it effectively captures the conditions outlined in the problem statement, setting the left side as the value associated with three times the width and the constant, while the right side relates to four times the width plus the additional seven.

Thus, the correct answer is