Answer :
To determine the number of hours Jiao works as a teacher, \( y \), we start by setting up the conditions given in the problem:
1. Jiao works at least 36 hours per week in total.
2. Jiao earns $15 per hour as a science tutor and $25 per hour as a teacher.
Let's denote:
- \( x \): Number of hours Jiao works as a science tutor.
- \( y \): Number of hours Jiao works as a teacher.
From the problem statement, we have the following equations based on the total hours and the earnings:
\[ x + y \geq 36 \]
\[ 15x + 25y \] (Total earnings per week)
To solve for \( y \), the number of hours Jiao works as a teacher, we need to consider the minimum scenario where \( x \) (hours worked as a science tutor) is maximized given the constraint \( x + y \geq 36 \).
Assuming \( x \) is maximized while satisfying \( x + y = 36 \) (to meet the minimum total hours requirement), then:
\[ x = 36 - y \]
Now, substituting this into the earnings equation:
\[ 15x + 25y = 15(36 - y) + 25y \]
\[ 15 \cdot 36 - 15y + 25y \]
\[ 540 + 10y \]
To maximize \( y \), we need to satisfy the condition \( x = 36 - y \geq 0 \):
\[ 36 - y \geq 0 \]
\[ y \leq 36 \]
Therefore, the minimum number of hours \( y \) that Jiao works as a teacher is at least:
\[ \boxed{36} \]
This means Jiao must work at least 36 hours as a teacher per week to satisfy the total minimum hours requirement of 36 hours per week and maximize her earnings.Answer:
Step-by-step explanation:
