## Math Problem Examples: Correct and Incorrect Solutions ### Overview The image presents three math problems, each with a question and a step-by-step solution. For two of the problems, a "prompt" is provided, and for the third, a "question" is provided. Below each problem, there are two attempted solutions, one marked with a red "X" indicating an incorrect solution, and the other marked with a green checkmark indicating the correct solution. ### Components/Axes * **Problem 1 (Top-Left):** * Question: Mark's father gave him $85. Mark bought 10 books, each of which cost $5. How much money does Mark have left? * Correct Solution (Green Check): Mark has $85, spends 10 x $5 = $50. $85 - $50 = $35 left. * Incorrect Solution (Red X): Not present in this problem. * Label: "prompt 1" * **Problem 2 (Top-Right):** * Question: Nancy has saved 4900 cents from selling lemonade. How many dollars does Nancy have? * Correct Solution (Green Check): Nancy saved 4900 cents, which means she saved 4900 / 100 = 49 dollars. * Incorrect Solution (Red X): Not present in this problem. * Label: "prompt 2" * **Problem 3 (Bottom):** * Question: The value of a sport utility vehicle this year is 16,000 dollars, which is 0.8 of what its value was last year. How much is the value of the vehicle last year? * Correct Solution (Bottom-Right, Green Check): The problem tells us that the value of the sport utility vehicle this year is $16,000, which is 0.8 times its value last year. This means that the value last year is $16,000 / 0.8 = $20,000. * Incorrect Solution (Bottom-Left, Red X): The problem tells us that the value of the sport utility vehicle this year is 16,000 dollars, which is 0.8 of what it was last year. So, if we multiply the value of the vehicle this year by 0.8, we get the value of the vehicle last year = 16,000 x 0.8 = 12,800 dollars. * Label: "question" ### Detailed Analysis or ### Content Details * **Problem 1:** * The correct solution calculates the total cost of the books (10 * $5 = $50) and subtracts it from the initial amount ($85 - $50 = $35). * **Problem 2:** * The correct solution converts cents to dollars by dividing by 100 (4900 / 100 = 49). * **Problem 3:** * The incorrect solution multiplies the current value by 0.8, which is the wrong operation. * The correct solution divides the current value by 0.8 to find the original value ($16,000 / 0.8 = $20,000). ### Key Observations * Each problem presents a word problem followed by a step-by-step solution. * The incorrect solutions demonstrate common errors in problem-solving. * The correct solutions clearly show the steps to arrive at the correct answer. ### Interpretation The image serves as an educational tool, illustrating how to solve basic math problems. It highlights the importance of understanding the problem and choosing the correct mathematical operation. The inclusion of incorrect solutions helps to identify potential pitfalls and reinforces the correct approach. The problems cover basic arithmetic operations such as multiplication, subtraction, and division, as well as unit conversion (cents to dollars).