Mini Exercise Questions – Cost of sales Q2

I’m having trouble calculating the opening & closing stock on Mini Exercise Questions – Cost of sales Q2

Sales of $450k with gross margin of 15%
Gross profit (450 x 15%) $67.5
Cost of sales $382.5

Purchases $400k
Closing stock 30% higher than opening stock?

I’m having trouble working out the opening & closing stock?
From the book the answers are:
opening stock =$58.33
Closing stock = $75.83

Thanks
Jonathan