## Math Problem Solution Comparison ### Overview The image presents a math problem and two different attempts to solve it. The problem involves calculating the total number of bolts needed to make a robe, given that it takes 2 bolts of blue fiber and half that much white fiber. One solution is marked as incorrect (X), while the other is marked as correct (checkmark). ### Components/Axes * **Question:** "A robe takes 2 bolts of blue fiber and half that much white fiber. How many bolts in total does it take?" * **Incorrect Solution (Top):** Presented in a grey box with a red "X" icon in the bottom right. * **Correct Solution (Bottom):** Presented in a light green box with a green checkmark icon in the bottom right. ### Detailed Analysis or ### Content Details **Incorrect Solution (Top):** * **Initial Statement (Blue Highlighted):** "To find the total number of bolts needed for the robe, we need to calculate the total amount of blue fiber and white fiber required, and then divide that by the amount of blue fiber required per bolt. The problem states that a robe takes 2 bolts of blue fiber and half that much white fiber." * **Blue Fiber Calculation (Red Highlighted):** "To find the total amount of blue fiber required, we can multiply the number of bolts by the amount of blue fiber per bolt: 2 bolts x 2 = 4 bolts of blue fiber" * **White Fiber Calculation (Red Highlighted):** "To find the total amount of white fiber required, we can multiply the number of bolts by the amount of white fiber per bolt: 2 bolts x 0.5 = 1 bolt of white fiber" * **Division Step (Red Highlighted):** "Now, we need to divide the total amount of blue fiber by the amount of blue fiber required per bolt to find the total number of bolts needed: 4 bolts of blue fiber / 2 = 2 bolts of blue fiber per bolt" * **Conclusion:** "Therefore, it takes 2 bolts of blue fiber and 1 bolt of white fiber to make the robe." **Correct Solution (Bottom):** * **Initial Statement (Blue Highlighted):** "To find the total number of bolts needed for the robe, we need to calculate the total amount of blue fiber and white fiber required, and then divide that by the amount of blue fiber required per bolt. The problem states that a robe takes 2 bolts of blue fiber and half that much white fiber." * **Blue Fiber Calculation (Green Highlighted):** "So, the total amount of blue fiber required is 2 bolts x 1 bolt = 2 bolts." * **White Fiber Calculation (Green Highlighted):** "The total amount of white fiber required is half of 2 bolts, which is 1 bolt." * **Final Calculation (Green Highlighted):** "Therefore, the total number of bolts needed for the robe is 2 + 1 = 3 bolts." ### Key Observations * The incorrect solution attempts to calculate the amount of blue fiber per bolt, which is not necessary to solve the problem. * The correct solution directly calculates the amount of blue and white fiber needed and sums them to find the total number of bolts. * The initial statement in both solutions is identical. ### Interpretation The image highlights a common mistake in problem-solving: overcomplicating the solution. The incorrect solution introduces an unnecessary division step, leading to an incorrect conclusion. The correct solution demonstrates a more straightforward and efficient approach to solving the problem. The problem requires calculating the total number of bolts, which is the sum of the blue and white fiber bolts. Since the robe takes 2 bolts of blue fiber and half that amount of white fiber (1 bolt), the total number of bolts is 2 + 1 = 3.