To determine the amount of sales Juan needs in order for the two earning options to pay the same amount, we need to set up equations for both earning options and find the point where they are equal.
Let's denote [tex]\( x \)[/tex] as the amount of Juan's sales in dollars.
### Option 1:
Juan earns [tex]$200 per week plus 15% commission on his sales. Therefore, his earnings with this option can be expressed as:
\[ \text{Earnings Option 1} = 200 + 0.15x \]
### Option 2:
Juan earns $[/tex]300 per week plus 10% commission on his sales. Therefore, his earnings with this option can be expressed as:
[tex]\[ \text{Earnings Option 2} = 300 + 0.10x \][/tex]
### Finding the Point where Earnings are Equal:
To find the sales amount where both options provide the same earnings, we set the two equations equal to each other:
[tex]\[ 200 + 0.15x = 300 + 0.10x \][/tex]
### Solving the Equation:
First, we isolate the term involving [tex]\( x \)[/tex] by moving all [tex]\( x \)[/tex]-terms to one side and constants to the other side:
[tex]\[ 0.15x - 0.10x = 300 - 200 \][/tex]
[tex]\[ 0.05x = 100 \][/tex]
Next, we solve for [tex]\( x \)[/tex] by dividing both sides by 0.05:
[tex]\[ x = \frac{100}{0.05} \][/tex]
[tex]\[ x = 2000 \][/tex]
So, Juan's sales need to be [tex]$2000 for the two earning options to pay the same amount.
Therefore, the correct answer is:
\[ \boxed{2000} \]
### Answer:
B. $[/tex]2,000
