To determine the amount Rita earns in a year, given that she earns [tex]\(x\)[/tex] each week, we need to recognize how many weeks there are in a year. There are typically 52 weeks in a year.
Let's derive the expression step-by-step:
1. Weekly Earnings:
Rita earns [tex]\(x\)[/tex] dollars each week.
2. Number of Weeks in a Year:
There are 52 weeks in a year.
3. Annual Earnings:
To find her total earnings in a year, you need to multiply her weekly earnings by the number of weeks in a year. Thus, the expression will be [tex]\(x\)[/tex] multiplied by 52.
Hence, the yearly earnings can be represented as:
[tex]\[
52 \times x \text{ or simply } 52x
\][/tex]
Now, let's evaluate the given options:
- [tex]\(x + 52\)[/tex]: This represents only adding 52 to her weekly earnings, not multiplying it by the number of weeks.
- [tex]\(52 - x\)[/tex]: This represents subtracting her weekly earnings from 52, which doesn’t relate to total annual earnings.
- [tex]\(\frac{x}{52}\)[/tex]: This implies dividing her weekly earnings by 52, which would tell us the weekly earnings spread over a year, not the total annual amount.
- [tex]\(52x\)[/tex]: This correctly represents her annual earnings by multiplying her weekly earnings by the number of weeks in a year.
Therefore, the correct expression that represents the amount Rita earns in a year is:
[tex]\[
52x
\][/tex]
