Answer :
To solve this problem, we need to model Lin's weekly earnings and the conditions of her job in a mathematical expression.
1. Identify the Components:
- Hourly Rate: Lin earns [tex]$8.25 for each hour she works.
- Transportation Allowance: Lin gets a fixed $[/tex]10 allowance per week.
- Minimum Work Hours: She needs to work at least 5 hours a week.
- Maximum Earnings: Lin can earn up to [tex]$175 per week, including her transportation allowance.
2. Mathematical Representation:
- Earnings Expression: Lin's earnings per week can be represented as \(8.25h + 10\), where \(h\) is the number of hours she works.
- Earnings Condition: These earnings should be less than or equal to $[/tex]175, which gives us the inequality:
[tex]\[
8.25h + 10 \leq 175
\][/tex]
- Minimum Hours Condition: Lin must work more than 5 hours a week:
[tex]\[
h > 5
\][/tex]
3. Select the Correct Option:
- The situation is represented by the inequality [tex]\(8.25h + 10 < 175\)[/tex] and the condition [tex]\(h > 5\)[/tex].
Therefore, the correct answer is: [tex]\(8.25h + 10 < 175\)[/tex] and [tex]\(h > 5\)[/tex].
1. Identify the Components:
- Hourly Rate: Lin earns [tex]$8.25 for each hour she works.
- Transportation Allowance: Lin gets a fixed $[/tex]10 allowance per week.
- Minimum Work Hours: She needs to work at least 5 hours a week.
- Maximum Earnings: Lin can earn up to [tex]$175 per week, including her transportation allowance.
2. Mathematical Representation:
- Earnings Expression: Lin's earnings per week can be represented as \(8.25h + 10\), where \(h\) is the number of hours she works.
- Earnings Condition: These earnings should be less than or equal to $[/tex]175, which gives us the inequality:
[tex]\[
8.25h + 10 \leq 175
\][/tex]
- Minimum Hours Condition: Lin must work more than 5 hours a week:
[tex]\[
h > 5
\][/tex]
3. Select the Correct Option:
- The situation is represented by the inequality [tex]\(8.25h + 10 < 175\)[/tex] and the condition [tex]\(h > 5\)[/tex].
Therefore, the correct answer is: [tex]\(8.25h + 10 < 175\)[/tex] and [tex]\(h > 5\)[/tex].
