Eli sells refrigerators. His base salary is $250 per week, and his commission is $50 for each refrigerator (r) that he sells. He needs to make more than $900 this week. Which TWO statements are correct for this situation?

Question

Responses
A $50r + $250 < $900$50r + $250 < $900
B $50r — 250 > $900$50r — 250 > $900
C $50r + $250 > $900$50r + $250 > $900
D Eli needs to sell more than 13 refrigerators to earn more than $900 this week.Eli needs to sell more than 13 refrigerators to earn more than $900 this week.
E Eli needs to sell more than 15 refrigerators to earn more than $900 this week.Eli needs to sell more than 15 refrigerators to earn more than $900 this week.

Answer 1

To analyze Eli's earnings, we can express the total earnings equation based on his base salary and commission for the refrigerators sold.

Eli's total earnings can be represented as: \[ \text{Total Earnings} = 250 + 50r \]

He wants to earn more than $900, so we set up the inequality: \[ 250 + 50r > 900 \]

Now we can solve this inequality:

1. Subtract $250 from both sides: \[ 50r > 900 - 250 \] \[ 50r > 650 \]

2. Divide both sides by 50: \[ r > \frac{650}{50} \] \[ r > 13 \]

This means Eli needs to sell more than 13 refrigerators to earn more than $900.

Now, let's analyze the response options:

• A: \( 50r + 250 < 900 \)

  • This would mean he earns less than $900, which is incorrect for his goal.

• B: \( 50r - 250 > 900 \)

  • This is also incorrect because it does not represent the situation correctly.

• C: \( 50r + 250 > 900 \)

  • This is correct because it directly represents the requirement for Eli to earn more than $900.

• D: Eli needs to sell more than 13 refrigerators to earn more than $900 this week.

  • This is correct based on our calculation.

• E: Eli needs to sell more than 15 refrigerators to earn more than $900 this week.

  • This is incorrect, as he only needs to sell more than 13 refrigerators.

Thus, the TWO correct statements for this situation are:

C and D.