How Many Shares to Buy to Achieve a Target Average Price?

[Grimmet]

Writing a small python script...
If one owns 250000 shares at 0.005
and buys shares at 0.03.
How many shares would one buy for the average price to equal 0.02.

My attempt so far as used brute force looping to get close to a figure.
For example, the script gives the answer 375000 shares.
... I'm sure there's a more elegant way.

exitPrg = "y"

def LowBracket(buyP, targetP, currentA, ownedS, lim):
nX = 0
while nX <= limit:
nm = round(((nX * buyP)+currentA)/(nX+ownedS),5)
if nm == targetPrice:
break
nX += 1
return nX

def HighBracket(buyP, targetP, currentA, ownedS, lim):
nY = lim
while nY > 0:
nn = round(((nY * buyP)+currentA)/(nY+ownedS),5)
if nn == targetP:
break
nY -= 1
return nY

while ( exitPrg == "y" or exitPrg == "Y"):
ownedShares = input("\nShares owned: ")
boughtPrice = input("Price bought: ")
buyPrice = input("New price: ")
targetPrice = input("Target price: ")
limit = input("Share limit: ")

ownedShares = int(ownedShares)
boughtPrice = float(boughtPrice)
buyPrice = float(buyPrice)
targetPrice = float(targetPrice)
limit = int(limit)

currentAmount = ownedShares * boughtPrice

numberA = LowBracket(buyPrice, targetPrice, currentAmount, ownedShares, limit)

numberB = HighBracket(buyPrice, targetPrice, currentAmount, ownedShares, limit)

print("\nNumber of shares: %i\n" % ((numberB+numberA)/2))

exitPrg = input("Continue? (y/n) ")

Thanks.

 

[MarkFL]

You could use what's called a weighted average to determine the answer:

$$\frac{250000\cdot0.005+X\cdot0.03}{250000+X}=0.02$$

Simplify:

$$\frac{1250+0.03X}{250000+X}=0.02$$

Multiply through by $250000+X$:

$$1250+0.03X=5000+0.02X$$

Rearrange:

$$0.01X=3750$$

Multiply through by 100:

$$X=375000$$

 

[Grimmet]

Therefore:
Shares = ownedShares*targetPrice - ownedShares*boughtPrice / buyPrice - targetPrice

Thanks for the help.

Grimmet