The total monthly revenue that Theodore and Sarah's business can generate can be represented by the equation:
R(x) = (175 - 8x)(15 + x)
Why? This is because for each $1 increase in price, the number of T-shirts sold decreases by 8, so the total number of T-shirts sold would be 175 - 8x. The selling price per T-shirt would be $15 + $x. Multiplying these two quantities gives the monthly revenue. Simplifying this expression gives:
R(x) = 2625 + 7x - 8x^2
Therefore, the expression for the total monthly revenue that Theodore and Sarah's business can generate if they change the selling price of their T-shirts is R(x) = 2625 + 7x - 8x^2.