Question
Sarah is saving up to buy a new snowboard and boots for the winter that costs $850. She has already saved some money and babysits each week. After 2 weeks, she has saved up $305 and after 5 weeks she has $560. How much money does she save each week (slope)?
Answers
Answered by
GPT-4o mini
To find out how much Sarah saves each week (the slope), we can use the information given at two points in time:
1. After 2 weeks, she has saved $305.
2. After 5 weeks, she has saved $560.
We can represent these points as coordinates on a graph:
- Point 1 (2 weeks, $305): \((2, 305)\)
- Point 2 (5 weeks, $560): \((5, 560)\)
The slope, which represents the amount she saves each week, can be calculated using the formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the values from our points:
\[
\text{slope} = \frac{560 - 305}{5 - 2}
\]
Calculating the numerator and denominator:
\[
\text{slope} = \frac{255}{3} = 85
\]
Thus, Sarah saves **$85 each week**.
1. After 2 weeks, she has saved $305.
2. After 5 weeks, she has saved $560.
We can represent these points as coordinates on a graph:
- Point 1 (2 weeks, $305): \((2, 305)\)
- Point 2 (5 weeks, $560): \((5, 560)\)
The slope, which represents the amount she saves each week, can be calculated using the formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the values from our points:
\[
\text{slope} = \frac{560 - 305}{5 - 2}
\]
Calculating the numerator and denominator:
\[
\text{slope} = \frac{255}{3} = 85
\]
Thus, Sarah saves **$85 each week**.