Question

find the value of w in the diagram below. diagram showing a rectangle labeled 26, followed by five rectangles each labeled w, with the total length labeled 59

Explanation:

Step1: Set up the equation

The total length is 59, which is the sum of 26 and 5 times \( w \). So the equation is \( 26 + 5w = 59 \).

Step2: Subtract 26 from both sides

Subtract 26 from each side: \( 5w = 59 - 26 \). Calculating the right side, \( 59 - 26 = 33 \), so \( 5w = 33 \)? Wait, no, 59 - 26 is 33? Wait, 26 + 33 is 59? Wait, no, 26 + 33 is 59? Wait, 26 + 33 = 59? 26 + 30 = 56, plus 3 is 59. Yes. Then \( 5w = 33 \)? Wait, no, wait the diagram: 26 plus five \( w \)s equals 59. So \( 26 + 5w = 59 \). Subtract 26: \( 5w = 59 - 26 = 33 \)? Wait, no, 59 - 26 is 33? Wait, 26 + 33 is 59. Then divide both sides by 5: \( w = \frac{33}{5} \)? Wait, that can't be. Wait, maybe I made a mistake. Wait, 59 - 26: 59 - 20 = 39, 39 - 6 = 33. Yes. So \( 5w = 33 \), so \( w = 33/5 = 6.6 \)? Wait, but maybe the diagram is different. Wait, the left part is 26, then five \( w \)s, total 59. So equation: 26 + 5w = 59. Then 5w = 59 - 26 = 33. Then w = 33/5 = 6.6. Wait, but maybe I misread the numbers. Wait, the total is 59, left is 26, then five \( w \)s. So 26 + 5w = 59. Solve for w: 5w = 59 - 26 = 33. So w = 33/5 = 6.6. Wait, but maybe the numbers are different. Wait, maybe I miscalculated 59 - 26. 59 - 26: 59 - 20 = 39, 39 - 6 = 33. Yes. So 5w = 33, so w = 33/5 = 6.6. Wait, but maybe the diagram is 26 and five w's, total 59. So that's the equation.

Answer:

\( w = \frac{33}{5} = 6.6 \) (or as a fraction, \( \frac{33}{5} \) or 6.6)