help with cost of sales

Good morning Sir,
please kindly help with the working of your answers to the following.
Even after solving the problems and could not get the correct answers as compare to yours .
e.g in question 1 below, I could get the closing inventory but how you arrive at purchase figure I tried all my best but could not get the figure.

thanks

1 Cost of Sales
Question 1
A butcher sells $300,000 of meat at a consistent mark up of 25%. His inventory at the start of the year was $15,000. This had increased by
20% by the end of the year.
Calculate the purchases for the year.
Question 2
His rival down the road achieves a gross margin of 15%. His closing inventory was 30% higher than the opening inventory. Sales in the
year were $450,000 and purchases were $400,000.
What was the opening inventory?
Question 3
The local supermarket sold $500,000 worth of goods in January at a consistent mark up of 12½%. Opening inventory was $20,000 and
purchases in the month were $440,000.
How much was closing inventory?