<h3>The Main Idea</h3> <p><strong>Map the words to the formula, plug in what you know, solve for what you don't.</strong></p> <p>These problems give you a formula with letters and tell you what each letter means. Your job is to match the numbers from the story to the right letters, then calculate.</p> <h3>What is a Linear Model?</h3> <p>A linear model describes how a total is made up of parts. The most common form is:</p> <p style="text-align: center; font-size: 1.1em;"><strong>Total = (Rate × Quantity) + Starting Amount</strong></p> <p>This shows up everywhere: car rentals, phone plans, worker pay, water tanks. The formula might use different letters (E = mh + b, C = 15 + 0.10m, etc.), but the structure is always the same.</p> <h3>The Approach</h3> <ol> <li><strong>Read the question first</strong> — What are you looking for? The answer is hiding in the question sentence.</li> <li><strong>Find your target variable</strong> — Which letter represents what you're solving for?</li> <li><strong>Map the other values</strong> — Match each piece of information to its letter in the formula.</li> <li><strong>Plug in and solve</strong>: <ul> <li><strong>Working forward:</strong> If the target is already by itself (like E = mh + b), just plug in and calculate.</li> <li><strong>Working backward:</strong> If your target is buried in the formula, plug in everything else, then solve for it using opposite operations.</li> </ul> </li> </ol> <h3>Working Forward vs. Backward</h3> <p><strong>Forward (evaluate):</strong> The formula already equals what you want. Plug in and calculate.</p> <p>Example: Find E when E = mh + b, and you know m, h, and b.</p> <p><strong>Backward (solve):</strong> What you want is inside the formula. Plug in what you know, then solve for the unknown.</p> <p>Example: Find b when E = mh + b, and you know E, m, and h.</p> <p>Use opposite operations: addition ↔ subtraction, multiplication ↔ division.</p> <h3>Common Pitfall</h3> <p><strong>Plugging numbers into wrong places.</strong> Slow down and match each value to its letter. The problem defines what each letter means — use those definitions.</p>
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