CMIMC 2022 Algebra and Number Theory Division 1 Problem 2

A shipping company charges 0.30 l+0.40 w+0.50h dollars to process a right rectangular prism-shaped box with dimensions l, w, h in inches. The customers themselves are allowed to label the three dimensions of their box with l, w, h for the purpose of calculating the processing fee. A customer finds that there are two different ways to label the dimensions of their box B to get a fee of \$ 8.10, and two different ways to label B to get a fee of \$ 8.70. None of the faces of B are squares. Find the surface area of B, in square inches.