Question
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 money Sarah saves each week, we will calculate the slope using the information provided. The slope represents her weekly savings rate.
We have two points based on the information given:
1. After 2 weeks, Sarah has saved $305. Thus, the point is (2, 305).
2. After 5 weeks, Sarah has saved $560. Thus, the point is (5, 560).
The formula for the slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the values from our points:
- \(x_1 = 2\), \(y_1 = 305\)
- \(x_2 = 5\), \(y_2 = 560\)
Now, we can calculate the slope:
\[
m = \frac{560 - 305}{5 - 2} = \frac{255}{3} = 85
\]
Therefore, Sarah saves **$85 each week**.
We have two points based on the information given:
1. After 2 weeks, Sarah has saved $305. Thus, the point is (2, 305).
2. After 5 weeks, Sarah has saved $560. Thus, the point is (5, 560).
The formula for the slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the values from our points:
- \(x_1 = 2\), \(y_1 = 305\)
- \(x_2 = 5\), \(y_2 = 560\)
Now, we can calculate the slope:
\[
m = \frac{560 - 305}{5 - 2} = \frac{255}{3} = 85
\]
Therefore, Sarah saves **$85 each week**.