Final answer:
After calculating Mindy's minimum sales required to achieve an income of at least $1,500, accounting for a $48 shipping cost, it is determined that she would need to make sales of at least $3,870. Since this option is not provided, we look for the higher value, and the right answer is $4,320.
Step-by-step explanation:
To determine the minimum amount of sales Mindy must have to ensure her income is at least $1,500, we can set up an inequality. We know she earns income equal to 40% of her sales minus the shipping cost, which can be written as 0.4S - $48 ≥ $1,500, where S represents her sales. First, add $48 to both sides of the inequality to isolate the sales term:
0.4S ≥ $1,500 + $48
0.4S ≥ $1,548
Next, divide both sides by 0.4 to solve for S:
S ≥ $3,870
So, the least amount of sales Mindy must have to ensure her income is at least $1,500 is $3,870. Since $3,870 is not one of the given options, we look for the next option greater than this amount, which is $3,720. However, $3,720 would not be enough, as Mindy's income would be only $1,488 ($3,720 * 0.4 - $48). Therefore, the correct answer is $4,320 (option c), which would give her an income of exactly $1,500.