Final answer:
The question regarding the number of hours a DJ could play for $450 cannot be answered without the hourly rate charged by the DJ. The provided details about work hours and guaranteed income are irrelevant to this scenario.
Step-by-step explanation:
The student is asking about the amount of time a DJ could play given a budget of $450. Unfortunately, the provided information doesn't include the rate that a DJ charges per hour, which is essential to calculate the number of hours they can be hired with that budget. Without this rate, we can't provide a mathematical solution. The question seems to mix up information about a family's work hours and guaranteed income, which is unrelated to the hiring of a DJ.