A speaker system with a price of $300 is to be purchased with an intitial payment of $100 and weekly payments of $25. Which of the following is an equation which can be used to find the number of weekly payments, \(w\), required to complete the purchase?

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For linear equation word problems, we typically look for the initial value and rate. Since we are paying $25 per week, slope should be 25. The initial amount is $100, which can be considered the y-intercept. Plugging it into the slope-intercept equation gives us the answer.

$$y=mx+b$$ $$y=25x+100$$ $$\boxed{300=25w+100} $$

With a bit of mental math or arithmetic calculation, we can figure out that a weekly payment of $25 can be extended to be a 4-week payment of $100 or a 8-week payment of $200, which is the amount due after the initial $100 payment. The only equation which is valid when we plug in \(w=8\) is option 3.