lesson
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Imagine you have 15∗∗inyourpiggybank,andeveryFridayyouearn∗∗8 doing yard chores.
If a brand-new skateboard costs $63, how many weeks will you need to work before you can buy it?
Turning Words into Rules
A variable is a letter that stands for an unknown number, like x for weeks and y for total money.
When a pattern adds a repeating amount every time, we multiply that repeat rate by x and add our starting amount.
📊An interactive function machine diagram showing how a real-world pattern builds an equation. On the left, an input box labeled 'Weeks (x) = 3'. An arrow points into a machine labeled 'Pattern Rule: y = 8x + 15'. Inside the machine, steps show '(8 * 3) + 15 = 24 + 15'. An arrow exits to the right into an output box labeled 'Total Saved (y) = $39'. Use bright modern colors (card background #ffffff, border #e6e6e6, accent blue #2563eb, dark text #1e2945). Clean and responsive down to 350px width.
Since each week brings 8∗∗,savingforxweeksgives8 \times x(or8x).Addingthestarting∗∗15$ gives our equation: y=8x+15
How do we use this equation to solve our multi-step problem and find the exact number of weeks?
Solving Multi-Step Problems
To find when your savings equal **63∗∗,replacethetotalywith63$: 63=8x+15
First, subtract the starting 15 from both sides to find how much money still needs to be earned: 63−15=48.
Next, divide the remaining 48∗∗bytheweeklyrateof∗∗8: 48÷8=6 weeks.
📊A step-by-step visual solution flow for solving 63 = 8x + 15. Step 1: Show a balance scale or bar model with 63 on the left, and [8x] + [15] on the right. Step 2: Remove 15 from both sides, showing 48 = 8x. Step 3: Divide 48 into 8 equal parts of 6, concluding x = 6 weeks. High contrast colors, badge tags for 'Step 1: Subtract Start' and 'Step 2: Divide Rate', clean typography, responsive to 350px.