To determine the sales necessary for the salesperson to earn at least [tex]$600 in one week, we need to set up an inequality based on the given information:
1. The salesperson earns a fixed weekly salary of $[/tex]450.
2. The salesperson also earns an additional [tex]$15\%$[/tex] of her weekly sales.
We need to find the minimum sales [tex]\(x\)[/tex] such that her total earnings for the week are at least [tex]$600.
The total weekly earnings can be expressed by the equation:
\[ 450 + 0.15x \]
We need this to be at least $[/tex]600:
[tex]\[ 450 + 0.15x \geq 600 \][/tex]
Subtract 450 from both sides of the inequality to isolate the term involving [tex]\(x\)[/tex]:
[tex]\[ 0.15x \geq 600 - 450 \][/tex]
[tex]\[ 0.15x \geq 150 \][/tex]
Now, divide both sides by 0.15 to solve for [tex]\(x\)[/tex]:
[tex]\[ x \geq \frac{150}{0.15} \][/tex]
Performing the division gives:
[tex]\[ x \geq 1000 \][/tex]
Therefore, the sales necessary for the salesperson to earn at least $600 in one week is [tex]\(x \geq 1000\)[/tex].
The correct answer is:
C. [tex]\(x \geq 1000\)[/tex]
