2000 potatoes at 84 euro each is 90000 euros (my goodness they are expensive potatoes!)
X potatoes at 45 euros is 45X euros
Now we have 2000+X potatoes. And we want them to have an average price of 69 euros
So the total cost of all the potatoes will have to be 69(2000+X) euros.
so we have
\(2000 \times 84 + 45x = 69(2000+x)\\ 2000 \times 84 + 45x = 69\times 2000+69x\\ 2000 \times 84 -69\times 2000 = 69X-45x\\ 2000(84-69)=(69-45)x\\ x=\frac{2000(84-69)}{(69-45)}\\ x=\frac{30000}{24}\\ x=1250 potatoes\\ \)
check
(2000*84+1250*45)/3250 = 69 Good :)
So what do we have
\( x=\frac{2000(84-69)}{(69-45)}\\ \)
Let the original number of units be N So N=2000 potatoes
Let the original highher price be H so H=84 euros
Let the new low price be L so L = 45 euros
Let the desired average price be A so A= 69 euros
x is the additional number we need to buy to reduce the average price to the one that is desired.
and we have:
\(x=\frac{N(H-A)}{A-L}\)
.