To solve the problem, we need to determine the time [tex]\( t \)[/tex] when the water level [tex]\( W \)[/tex] becomes less than or equal to 64 cups, based on the given equation:
[tex]\[ W = -0.414t + 129.549 \][/tex]
Here's a step-by-step breakdown:
1. Set Up the Inequality: We need the water level [tex]\( W \)[/tex] to be less than or equal to 64 cups.
[tex]\[
-0.414t + 129.549 \leq 64
\][/tex]
2. Isolate the Term with [tex]\( t \)[/tex]: Subtract 129.549 from both sides of the inequality to isolate the term that includes [tex]\( t \)[/tex].
[tex]\[
-0.414t \leq 64 - 129.549
\][/tex]
[tex]\[
-0.414t \leq -65.549
\][/tex]
3. Solve for [tex]\( t \)[/tex]: Divide both sides of the inequality by -0.414. Note that since we are dividing by a negative number, we need to reverse the inequality sign.
[tex]\[
t \geq \frac{-65.549}{-0.414}
\][/tex]
4. Calculate the Division:
[tex]\[
t \geq 158.34
\][/tex]
5. Approximate the Time: We need to determine the closest option for the number of minutes from the given choices. The closest number to 158.34 minutes is 160 minutes.
6. Conclusion: Based on the calculated time and the choices provided, the water level would be less than or equal to 64 cups after approximately 160 minutes.
Therefore, the answer is:
[tex]\[
\boxed{160 \text{ minutes}}
\][/tex]
