To determine which two statements are correct for Eli's situation, let's first establish the inequality that represents the scenario.
Eli's total earnings for the week can be expressed as: \[ \text{Total Earnings} = \text{Base Salary} + \text{Commission} \] \[ \text{Total Earnings} = 250 + 50r \]
Eli wants to make more than $900, so we need to set up the inequality: \[ 250 + 50r > 900 \]
Now, let's solve this inequality for \( r \):
- Subtract 250 from both sides: \[ 50r > 900 - 250 \] \[ 50r > 650 \]
- Divide both sides by 50: \[ r > \frac{650}{50} \] \[ r > 13 \]
This tells us that Eli needs to sell more than 13 refrigerators to earn more than $900.
Now let's analyze the options:
A. \( 50r + 250 < 900 \)
This is incorrect because we need Eli's earnings to be greater than $900, not less.
B. \( 50r - 250 > 900 \)
This is incorrect because the expression does not represent his total earnings correctly.
C. \( 50r + 250 > 900 \)
This is correct as it reflects the correct condition for Eli's earnings.
D. Eli needs to sell more than 13 refrigerators to earn more than $900 this week.
This is correct as derived from our calculation.
E. Eli needs to sell more than 15 refrigerators to earn more than $900 this week.
This is incorrect because selling more than 13 refrigerators is sufficient; he does not need to sell more than 15.
The two correct statements are:
C. \( 50r + 250 > 900 \)
D. Eli needs to sell more than 13 refrigerators to earn more than $900 this week.