Working out ratio of 2 prices to equal the average selling price

Question

I understand my question might not have an exact answer but was wondering how I could best go about solving this.

So I have a Volume of product sold, 7000 units

I have an Average Selling Price of £8.81

I know the product was sold at 2 fixed prices, £10 and £6.67

Is there a way I can work out the ratio of units sold at each price? I have multiple variations of this scenario to work through!

I am familiar with Excel and Python to help along the calculating process! I have tried making a matrix of all prices but

Answer 1

Yes, you can.

Let's say you sold $7000$ units of $a$ and $b$.

So then $a+b=7000$.

Since the average selling price was $\$8.81$, you made a total of $\$61670$.

Then, let $10a+6.67b=61670$, since that is how much you made from each product.

Two variables and two equations should be simple to solve.