Final answer:
Situations A and B represent proportional relationships between hours worked and the amount earned for Matt and Jane because both situations have the same earning rate of $20 per hour for each individual.
Step-by-step explanation:
To determine which situation represents a proportional relationship between the hours worked and the amount earned for Matt and Jane, we need to compare the ratios of the amount earned to hours worked for both individuals. In a proportional relationship, these ratios should be equal. Here are the calculations:
- A) Matt's rate: $100 / 5 hours = $20 / hour, Jane's rate: $80 / 4 hours = $20 / hour. The rates are the same, so this represents a proportional relationship.
- B) Matt's rate: $120 / 6 hours = $20 / hour, Jane's rate: $80 / 4 hours = $20 / hour. The rates are the same, so this also represents a proportional relationship.
- C) Matt's rate: $150 / 5 hours = $30 / hour, Jane's rate: $100 / 3 hours = approximately $33.33 / hour. The rates are different, so this does not represent a proportional relationship.
- D) Matt's rate: is $140 / 7 hours = $20 / hour, and Jane's rate: is $100 / 4 hours = $25 / hour. The rates are different, so this does not represent a proportional relationship.
Therefore, both situations A and B represent a proportional relationship between the hours worked and the amount earned for Matt and Jane as they both have the same earning rate of $20 per hour.