Question

The high temperature outside one day is 100 degrees. The high temperature decreases at a constant rate of 4 degrees per week. How many weeks could have passed if the high temperature is now above 40 degrees?
Write an inequality to represent the situation. Use x to represent the number of weeks.

Answer 1

To model the situation, we start with the initial high temperature of 100 degrees. The temperature decreases at a constant rate of 4 degrees per week. Thus, after \( x \) weeks, the temperature can be expressed as:

\[
T = 100 - 4x
\]

We want to find the number of weeks, \( x \), such that the temperature is still above 40 degrees. This gives us the following inequality:

\[
100 - 4x > 40
\]

Now, we can solve this inequality for \( x \):

1. Subtract 100 from both sides:
\[
-4x > 40 - 100
\]
\[
-4x > -60
\]

2. Divide both sides by -4, remembering to reverse the inequality sign:
\[
x < 15
\]

This means that fewer than 15 weeks could have passed for the high temperature to still be above 40 degrees.

Thus, the inequality representing the situation is:

\[
100 - 4x > 40
\]
and the solution indicates \( x < 15 \).