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?

Question

Write an inequality to represent the situation. Use x to represent the number of weeks.

100−4x>40
Nice!
You just wrote an inequality to represent the situation. Now solve the associated equation, 100 - 4x = 40, to find the boundary for the inequality. Show your work or solve on paper.

100 - 4x > 40
100−4x
=
40


x
=

Answer 1

To solve the equation \(100 - 4x = 40\), follow these steps:

1. Start with the equation: \[ 100 - 4x = 40 \]

2. Isolate the term with \(x\): \[ 100 - 40 = 4x \] \[ 60 = 4x \]

3. Divide both sides by 4 to solve for \(x\): \[ x = \frac{60}{4} = 15 \]

So, the boundary for the inequality is \(x = 15\).

Now, interpret this result in the context of the original problem: if \(x\) is the number of weeks that have passed, then the temperature remains above 40 degrees as long as \(x < 15\).

Thus, you can conclude that the number of weeks that have passed, represented by \(x\), must be less than 15 weeks for the high temperature to be above 40 degrees: \[ x < 15 \]