Question
Ms. Jones is hiking. She starts at 40 feet and hikes up at a constant rate of 8 feet per minute. How many minutes could she be hiking if she is above 270 feet in elevation?
Write an inequality to represent the situation. Use x to represent the number of minutes.
40+8x>270
Excellent!
You just wrote an inequality to represent the situation. Now solve the associated equation, 40 + 8x = 270, to find the boundary for the inequality. Show your work or solve on paper.
40 + 8x > 270
40+8x
=
270
x
=
28.75
Excellent!
Now figure out if the boundary, x = 28.75, is a solution to the inequality. Does x = 28.75 make the inequality true or false?
40 + 8x > 270
True
False
You got it!
You found that x= 28.75 makes the inequality false. Now test x= 28 and x= 29. Do they make the inequality true or false?
x= 28x=28.75 (boundary)x= 2940 + 8x > 270
True
False
False
True
False
Write an inequality to represent the situation. Use x to represent the number of minutes.
40+8x>270
Excellent!
You just wrote an inequality to represent the situation. Now solve the associated equation, 40 + 8x = 270, to find the boundary for the inequality. Show your work or solve on paper.
40 + 8x > 270
40+8x
=
270
x
=
28.75
Excellent!
Now figure out if the boundary, x = 28.75, is a solution to the inequality. Does x = 28.75 make the inequality true or false?
40 + 8x > 270
True
False
You got it!
You found that x= 28.75 makes the inequality false. Now test x= 28 and x= 29. Do they make the inequality true or false?
x= 28x=28.75 (boundary)x= 2940 + 8x > 270
True
False
False
True
False
Answers
GPT-4o mini
Let's start by determining the results of substituting \( x = 28 \) and \( x = 29 \) into the inequality \( 40 + 8x > 270 \).
1. **For \( x = 28 \)**:
\[
40 + 8(28) > 270
\]
Calculate:
\[
40 + 224 = 264
\]
So,
\[
264 > 270 \quad \text{(False)}
\]
2. **For \( x = 29 \)**:
\[
40 + 8(29) > 270
\]
Calculate:
\[
40 + 232 = 272
\]
So,
\[
272 > 270 \quad \text{(True)}
\]
Now, we summarize the results:
- For \( x = 28 \), the inequality \( 40 + 8x > 270 \) is **False**.
- For \( x = 29 \), the inequality \( 40 + 8x > 270 \) is **True**.
This means that Ms. Jones must hike for more than 28.75 minutes in order to be above 270 feet in elevation. Therefore, the possible values for \( x \) that satisfy the inequality are \( x > 28.75 \).
1. **For \( x = 28 \)**:
\[
40 + 8(28) > 270
\]
Calculate:
\[
40 + 224 = 264
\]
So,
\[
264 > 270 \quad \text{(False)}
\]
2. **For \( x = 29 \)**:
\[
40 + 8(29) > 270
\]
Calculate:
\[
40 + 232 = 272
\]
So,
\[
272 > 270 \quad \text{(True)}
\]
Now, we summarize the results:
- For \( x = 28 \), the inequality \( 40 + 8x > 270 \) is **False**.
- For \( x = 29 \), the inequality \( 40 + 8x > 270 \) is **True**.
This means that Ms. Jones must hike for more than 28.75 minutes in order to be above 270 feet in elevation. Therefore, the possible values for \( x \) that satisfy the inequality are \( x > 28.75 \).