Playing with profit levers, part 3

Is there a faster way of solving this prompt? My answer is below.

A company has two product lines: shoes and dresses. The shoes account for 25% of revenue, and dresses 75%. The shoes have 40% margin, and dresses 20%. The company has fixed costs of $20M and profits of $20M. The CEO wants to improve profits to $25M by changing the sales mix towards more profitable shoes. Assuming the total revenue stays constant, what would the sales mix have to be for the CEO to reach her target?

Objective: New sales mix % = ?

Givens

1. Shoe Revenue (%) = 25%
2. Dress Revenue (%) = 75%
3. Shoe Margin = 40%
4. Dress Margin = 20%
5. FC = $20M
6. Profit = $20M
7. New Profit = $25M

Calculations

1. CM = Profit - FC = $20M + $20M = $40M
2. CMR = (25% * 40%) + (75% * 20%) = 25%
3. Revenue = CM / CMR = $40M / 25% = $160M
4. New CM = New Profit - FC = $25M + $20M = $45M
5. New CMR = $45M / $160M = 28%
6. New Shoe Share % = x
7. New Dresses Share % = 1 - x
8. Mix formula: (Shoe Margin * New Shoe Share) + (Dress Margin * New Dress Share) = New CMR ==> (0.4 * x) + (0.2 * (1 - x)) = 0.28 ==> x = 0.4 & 1 - x = 0.6
9. New Shoe Share: 40%
10. New Dress Share: 60%