Let w denote the number of weeks required. Since Samantha saves x dollars each week, the total money saved in w weeks is x · w dollars. Adding this to her initial 50 dollars gives the required cost of 250 dollars.

Let w denote the number of weeks required. Since Samantha saves x dollars each week, the total money saved in w weeks is x · w dollars. Adding this to her initial 50 dollars gives the required cost of 250 dollars.

Samantha is saving up to buy a new bicycle for 250. She already has 50 saved. Samantha plans to save x per week from her allowance. How many weeks (in terms of x) will it take Samantha to save enough money to buy the bicycle?

Answer: It will take Samantha $\frac{200}{x}$ weeks to save enough money to buy the bicycle.

Step-by-step solution

Step 1: Find the remaining amount to be saved

The total cost of the bicycle is $250$ dollars, and Samantha already has $50$ dollars saved. Subtracting the initial savings from the total cost gives the remaining amount she needs to save, which is $200$ dollars.

Step 2: Set up an equation for the total savings after w weeks

Let $w$ denote the number of weeks required. Since Samantha saves $x$ dollars each week, the total money saved in $w$ weeks is $x \cdot w$ dollars. Adding this to her initial $50$ dollars gives the required cost of $250$ dollars.

Step 3: Solve for the number of weeks w in terms of x

Subtracting $50$ from both sides gives $x \cdot w = 200$ . Dividing both sides by $x$ isolates the variable $w$ , giving the total number of weeks in terms of $x$ .

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