Question

arnav starts with 5 dollars in his account. he earns 10 dollars per hour mowing lawns and deposits the earnings into his account. sarah starts with -15 dollars in her account. she earns 10 dollars per hour mowing lawns and deposits the earnings into her account. arnav: ( d = 5 + 10x ) the slope of arnav’s line is 10. sarah: ( d = -15 + 10x ) the slope of sarah’s line is 10. they both started with $10 in their accounts. arnav always has $10 more in his account than sarah. they both earn $10 per hour.

Explanation:

To determine the correct statements, we analyze each one:

Statement 1: "They both started with $10 in their accounts."

• Arnav starts with $5 (from \( d = 5 + 10x \), when \( x = 0 \), \( d = 5 \)).
• Sarah starts with $-15 (from \( d = -15 + 10x \), when \( x = 0 \), \( d = -15 \)).

Thus, this statement is false.

Statement 2: "Arnav always has $10 more in his account than Sarah."

Subtract Sarah’s balance from Arnav’s:
\( (5 + 10x) - (-15 + 10x) = 5 + 10x + 15 - 10x = 20 \).
Arnav has $20 more, not $10. Thus, this statement is false.

Statement 3: "They both earn $10 per hour."

• Arnav’s equation: \( d = 5 + 10x \). The coefficient of \( x \) (slope) is 10, meaning he earns $10 per hour.
• Sarah’s equation: \( d = -15 + 10x \). The coefficient of \( x \) (slope) is 10, meaning she earns $10 per hour.

Thus, this statement is true.

Answer:

The true statement is: They both earn $10 per hour.