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Yvonne is a salesperson who earns a fixed amount of [tex]\$1,850[/tex] per month. She also earns a commission of [tex]4\%[/tex] on the amount of goods that she sells. If she wants to earn more than [tex]\$2,300[/tex] in one month, how many dollars [tex](x)[/tex] in goods must she sell?

A. [tex]x \ \textgreater \ 4,150[/tex]

B. [tex]x \ \textgreater \ 11,250[/tex]

C. [tex]x \ \textgreater \ 10,050[/tex]

D. [tex]x \ \textless \ 11,250[/tex]

Sagot :

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]