Question
Wyatt is saving up to buy a new bike. He has $135 saved so far. He needs to save at least $115 more to afford a new bike.
Let m represent the amount of money, in dollars, that Wyatt still needs to save. Which inequality models the story?
Graph the inequality that models the story.
To draw a ray, plot an endpoint and select an arrow. Select an endpoint to change it from closed to open. Select the middle of the ray to delete it.
Let m represent the amount of money, in dollars, that Wyatt still needs to save. Which inequality models the story?
Graph the inequality that models the story.
To draw a ray, plot an endpoint and select an arrow. Select an endpoint to change it from closed to open. Select the middle of the ray to delete it.
Answers
GPT-4o mini
To find the inequality that models the situation, we start by noting the total amount of money Wyatt needs to save for the bike. He currently has $135 saved and needs at least $115 more to afford the bike.
Let \( m \) represent the amount of money Wyatt still needs to save. The total amount of money he will have after saving \( m \) more dollars can be expressed as:
\[
135 + m
\]
Since Wyatt needs at least $115 more, we can express this relationship with the inequality:
\[
135 + m \geq 250
\]
Here, \( 250 \) is the total amount he needs ($135 current savings + $115 needed). To isolate \( m \):
1. Subtract 135 from both sides:
\[
m \geq 250 - 135
\]
2. Simplify:
\[
m \geq 115
\]
Thus, the inequality that models the story is:
\[
m \geq 115
\]
### Graphing the Inequality
When graphing the inequality \( m \geq 115 \):
1. Start by drawing a number line.
2. Plot the point at \( m = 115 \). Since this is a "greater than or equal to" inequality, you will use a closed dot to indicate that \( 115 \) is included in the solution set.
3. Shade the line to the right of \( 115 \) to represent all values greater than \( 115 \) (i.e., \( m \) can be equal to or greater than \( 115 \)).
Here's a description of how to visualize the graph:
- The closed dot at \( 115 \) indicates \( m = 115 \) is part of the solution.
- An arrow extending to the right indicates that \( m \) can be greater than \( 115 \).
Make sure to properly label the number line for clarity.
Let \( m \) represent the amount of money Wyatt still needs to save. The total amount of money he will have after saving \( m \) more dollars can be expressed as:
\[
135 + m
\]
Since Wyatt needs at least $115 more, we can express this relationship with the inequality:
\[
135 + m \geq 250
\]
Here, \( 250 \) is the total amount he needs ($135 current savings + $115 needed). To isolate \( m \):
1. Subtract 135 from both sides:
\[
m \geq 250 - 135
\]
2. Simplify:
\[
m \geq 115
\]
Thus, the inequality that models the story is:
\[
m \geq 115
\]
### Graphing the Inequality
When graphing the inequality \( m \geq 115 \):
1. Start by drawing a number line.
2. Plot the point at \( m = 115 \). Since this is a "greater than or equal to" inequality, you will use a closed dot to indicate that \( 115 \) is included in the solution set.
3. Shade the line to the right of \( 115 \) to represent all values greater than \( 115 \) (i.e., \( m \) can be equal to or greater than \( 115 \)).
Here's a description of how to visualize the graph:
- The closed dot at \( 115 \) indicates \( m = 115 \) is part of the solution.
- An arrow extending to the right indicates that \( m \) can be greater than \( 115 \).
Make sure to properly label the number line for clarity.