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?

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.

1 answer

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 \( r \):

  1. Subtract 250 from both sides: \[ 50r > 900 - 250 \] \[ 50r > 650 \]
  2. 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.