Lucy's goal for her cycling class at the gym is to burn 450 calories in one hour. the number of calories (c) she actually burns in one hour varies no more than 45 calories. which inequality below represents this scenario?

a. |c - 450| ≤ 45
b. |c + 450| ≥ 45
c. |c - 45| ≤ 450
d. |c - 45| ≥ 450

The correct answer is:

A. |c - 450| ≤ 45  

Explanation:

Lucy's goal is 450 and the number of calories she actually burns is c.  The difference between her goal and the number she actually burns is no more than 45; this is where the expression c-450 comes from, as well as the less than or equal to 45.  However, we are not told that she always burns more or always burns less than her goal; therefore we must consider both, and this leads to our absolute value inequality.