Question

Lucy's goal for her cycling class at the gym is to burn 450 calories in one hour. The number of calories, c, she burns in one hour varies from her goal by no more than 45. Which inequality represents this statement?

a) |c - 450| ≤ 45
b) c ≥ 450 + 45
c) c ≤ 450 - 45
d) c = 450 + 45

Answer 1

The correct inequality that represents Lucy's goal for her cycling class to burn 450 calories with an allowed variance of 45 calories is |c - 450| ≤ 45.

Step-by-step explanation:

Lucy's goal is to burn 450 calories in one hour, and the number of calories, c, she burns can vary by no more than 45 calories from this goal. This means that the value of c can be either 45 calories less than or 45 calories more than 450. In mathematical terms, this is expressed as the absolute value inequality |c - 450| ≤ 45, which states that the absolute difference between the number of calories burned (c) and the goal (450) must be less than or equal to 45. Therefore, the correct inequality representing this statement is option (a) |c - 450| ≤ 45.