Chelsea dog-sits for her neighbors as a part-time job. She charges $12 a day plus an additional $2.50 for each walk she takes with he dogs. Determine which graph and which equation represent the amount of money Chelsea earns in one day, A, after taking W walks with he dogs.

Equations:
1. A=2.5w+12
2. A=2.5+12w
3.A=(12 + 2.5)w
4.A= 12-2.5w

1 answer

To determine the correct equation that represents the amount of money Chelsea earns in one day (A) after taking W walks with the dogs, we need to analyze the components of her earnings:

  • Chelsea charges $12 for the day.
  • For each walk, she charges an additional $2.50.

The total amount Chelsea earns can be represented as:

Total Earnings = Fixed Daily Charge + Charge for Walks

This can be formulated as:

\[ A = 12 + 2.5W \]

Where:

  • A is the total amount of money Chelsea earns in one day.
  • W is the number of walks she takes.

Comparing this with the provided equations:

  1. A = 2.5W + 12 (Correct: This directly matches our formulation)
  2. A = 2.5 + 12W (Incorrect: This implies $2.50 is constant and $12 is multiplied by the number of walks)
  3. A = (12 + 2.5)W (Incorrect: This implies that she earns the combined $14.50 for each walk)
  4. A = 12 - 2.5W (Incorrect: This suggests that her earnings decrease with the number of walks)

Therefore, the correct equation that represents Chelsea's earnings is:

A = 2.5W + 12

The graph representing this equation would be a straight line with a y-intercept of 12, rising with a slope of 2.5.