Question
Sarah is hiking. She starts at 80 feet and hikes up at a constant rate of 4 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.
80+4x>270
Good work!
You just wrote an inequality to represent the situation. Now solve the associated equation, 80 + 4x = 270, to find the boundary for the inequality. Show your work or solve on paper.
80 + 4x > 270
80+4x
=
270
x
=
Write an inequality to represent the situation. Use x to represent the number of minutes.
80+4x>270
Good work!
You just wrote an inequality to represent the situation. Now solve the associated equation, 80 + 4x = 270, to find the boundary for the inequality. Show your work or solve on paper.
80 + 4x > 270
80+4x
=
270
x
=
Answers
GPT-4o mini
To solve the equation \(80 + 4x = 270\), we'll follow these steps:
1. Subtract 80 from both sides of the equation:
\[
80 + 4x - 80 = 270 - 80
\]
This simplifies to:
\[
4x = 190
\]
2. Next, divide both sides by 4:
\[
x = \frac{190}{4}
\]
Calculating the division gives:
\[
x = 47.5
\]
Thus, the boundary for the inequality is \(x = 47.5\).
Now, to find the context of the original inequality \(80 + 4x > 270\):
- Sarah can hike for more than 47.5 minutes to be above 270 feet in elevation.
In conclusion, if \(x\) is the number of minutes Sarah hikes, then:
- \(x > 47.5\) means she is above 270 feet in elevation.
1. Subtract 80 from both sides of the equation:
\[
80 + 4x - 80 = 270 - 80
\]
This simplifies to:
\[
4x = 190
\]
2. Next, divide both sides by 4:
\[
x = \frac{190}{4}
\]
Calculating the division gives:
\[
x = 47.5
\]
Thus, the boundary for the inequality is \(x = 47.5\).
Now, to find the context of the original inequality \(80 + 4x > 270\):
- Sarah can hike for more than 47.5 minutes to be above 270 feet in elevation.
In conclusion, if \(x\) is the number of minutes Sarah hikes, then:
- \(x > 47.5\) means she is above 270 feet in elevation.