To determine which equation correctly represents Sarah's daily income, we need to consider both her base salary and the tips she receives.
1. Base Salary:
- Sarah earns a fixed amount of \[tex]$50 each day. This means that regardless of how much money is spent by her customers, she will always earn \$[/tex]50 per day as a base salary.
2. Tips:
- Sarah earns tips that are 15% of the total amount her customers spend on services. This means that if her customers spend an amount represented by [tex]\(x\)[/tex] dollars, then she earns [tex]\(15\%\)[/tex] of [tex]\(x\)[/tex].
- The percentage should be converted into decimal form for easier calculation. [tex]\(15\%\)[/tex] is equivalent to [tex]\(0.15\)[/tex].
3. Total Daily Income:
- Combining her base salary and her earnings from tips, we get Sarah’s total daily income.
- If [tex]\(y\)[/tex] represents Sarah’s total daily income, we can construct the equation by adding her base salary to her earnings from tips.
So, the equation for Sarah's daily income, [tex]\(y\)[/tex], in terms of the total amount [tex]\(x\)[/tex] her customers spend, is:
[tex]\[ y = 50 + 0.15x \][/tex]
To match the standard format of the options given:
[tex]\[ y = 0.15x + 50 \][/tex]
Thus, the correct equation representing Sarah's daily income is:
[tex]\[ \boxed{y = 0.15x + 50} \][/tex]
