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Hey there! Ready to become a master problem solver? Let's explore a simple, powerful model to tackle any challenge step by step.
Every big challenge becomes easier when you break it down. To solve problems like a pro, we use a five-step model: analyze, plan, solve, justify, and evaluate.
First, you analyze the information to find what is given and what is missing. Then, you formulate a clear strategy before you jump into doing any math.
After finding your solution, you must justify it by showing your work. Finally, evaluate your process to make sure your answer makes sense in the real world.
A local community garden is building a rectangular vegetable patch. The length must be 5 meters longer than the width. The total fencing available to surround the patch is 30 meters. What should the dimensions of the garden be?
- Analyze: Identify the given information. The perimeter (total fencing) is 30 meters. The length (L) is equal to the width (W) plus 5 meters: L = W + 5.
- Plan: Formulate a strategy using the perimeter formula, P = 2L + 2W. Substitute (W + 5) for L in the formula to create an equation with one variable.
- Solve: Write the equation: 30 = 2(W + 5) + 2W. Simplify to 30 = 2W + 10 + 2W, which becomes 30 = 4W + 10. Subtract 10 from both sides to get 20 = 4W, meaning W = 5 meters. Thus, the length L = 5 + 5 = 10 meters.
- Justify: Check your math by plugging the dimensions back into the perimeter formula. 2(10) + 2(5) = 20 + 10 = 30 meters. The math is correct.
- Evaluate: Think about the real-world scenario. A garden patch that is 10 meters by 5 meters is highly reasonable and fits the 30-meter fencing limit perfectly.