Let's solve the problem step by step to determine how many dollars in goods Yvonne must sell to make more than [tex]$2,300 in one month.
1. Identify Fixed Salary and Desired Salary:
- Yvonne's fixed salary: $[/tex]\[tex]$ 1,850$[/tex] per month.
- Desired total earnings: [tex]$\$[/tex] 2,300[tex]$ per month.
2. Calculate the Additional Amount Needed:
- Yvonne's fixed salary already covers part of her desired earnings. The additional amount she needs to earn through commissions is:
\[
\text{Additional Amount} = \text{Desired Salary} - \text{Fixed Salary}
\]
\[
\text{Additional Amount} = 2,300 - 1,850 = \$[/tex] 450
\]
3. Understand the Commission Rate:
- Yvonne earns a commission of [tex]\(4\%\)[/tex] (or [tex]\(0.04\)[/tex]) on the value of the goods she sells.
4. Set Up the Equation:
To find the amount of goods [tex]\( x \)[/tex] she needs to sell to earn at least \[tex]$450 in commission, we set up the equation where the commission earned is the additional amount needed:
\[
\text{Commission} = 0.04 \times x = 450
\]
5. Solve for \( x \):
\[
x = \frac{450}{0.04}
\]
6. Calculate \( x \):
\[
x = 11,250
\]
Therefore, Yvonne must sell more than $[/tex]\[tex]$ 11,250$[/tex] in goods to earn more than [tex]$\$[/tex] 2,300$ in one month.
The correct answer is:
B. [tex]\( x > 11,250 \)[/tex]
