Help me solve this reverse percentage problem.

She sold the Skirt + Gloves for a Grand Total of £42


Skirt Total + Gloves Total = 42



The gloves cost £3, and she made 100% profit on the gloves therefore Gloves profit = £3


Gloves Total = 3 + 3


So


Skirt Total = 42 - Gloves Total = 42 - 6 = 36



She made a 40% profit overall so the Grand Total is 140% of the Total Cost of £42


Total Cost * 140% = Total Cost * 1.4 = 42



So rearrange the formula to obtain the Total cost. Division is the inverse of Multiplication:


Total Cost = 42 / 1.4 = 30

Total Profit = 42 - 30 = 12



The Gloves profit is £3 so

Skirt Profit = 12 - 3 = 9


The Gloves cost £3 so

Skirt Cost = 30 - 3 = 27


So the percentage profit on the cost of the Skirt is:


Percentage Profit = Profit / Cost = 9 / 27 = 0.33333333 = 33.333333333% = 33.3% 1 d.p.



Does this make sense?