Question
Mrs. Prescott collects donations for a walk-a-thon fundraiser. A group of sponsors will donate $50 no matter how far she walks. Another group of sponsors will donate a total of $10 for each mile she walks. How many miles, x, could she walk to raise at least $170?
We'll write an inequality to represent this situation. The left side will represent the amount that Mrs. Prescott collects. Start by representing the amount of money that the group of sponsors will donate no matter how far she walks.
?
We'll write an inequality to represent this situation. The left side will represent the amount that Mrs. Prescott collects. Start by representing the amount of money that the group of sponsors will donate no matter how far she walks.
?
Answers
GPT-4o mini
To represent the situation mathematically, we need to combine the donations from both groups of sponsors.
1. The first group of sponsors donates a fixed amount of $50.
2. The second group of sponsors donates $10 for each mile, which can be represented as \(10x\), where \(x\) is the number of miles Mrs. Prescott walks.
So, the total amount Mrs. Prescott collects can be expressed as:
\[
50 + 10x
\]
We want this total amount to be at least $170. Therefore, we can set up the inequality as follows:
\[
50 + 10x \geq 170
\]
This inequality represents the situation where Mrs. Prescott collects enough money from her walk-a-thon fundraiser. You can now solve this inequality to find out how many miles she needs to walk.
1. The first group of sponsors donates a fixed amount of $50.
2. The second group of sponsors donates $10 for each mile, which can be represented as \(10x\), where \(x\) is the number of miles Mrs. Prescott walks.
So, the total amount Mrs. Prescott collects can be expressed as:
\[
50 + 10x
\]
We want this total amount to be at least $170. Therefore, we can set up the inequality as follows:
\[
50 + 10x \geq 170
\]
This inequality represents the situation where Mrs. Prescott collects enough money from her walk-a-thon fundraiser. You can now solve this inequality to find out how many miles she needs to walk.