Help Please! Practical equation solving for work

Question

Hello! I am at work and trying to find a formula for calculating the number of shares of a stock to buy, after the price has fluctuated from your original buy in, to give you your chosen average price per share. I think I am close in coming up with this equation: y=(ab+cx)/(a+x). All variables are known except for x. x is the solution, but I cannot find out how to solve for x.

 

Here are additional details I have constructed with a sample problem I worked out the long way:

 

numbers from sample problem in bold

 

these variables are known at the onset

a = initial number of shares bought = 100

b = initial price of each share = 13

c = fluctuated price of share = 10

y = goal average price = 10.5

 

these variables are unknown. We are searching for x

m = total spent on all shares  = 6,300

n = total shares bought = 600

x = number of shares to buy = 500

 

correlations already found:

• y=m/n
• n=m/y
• m=y*n

 

• a=n-x
• n=x+a
• x=n-a

 

• m=ab+cx
• ab=m-cx
• a=(m-cx)/b
• b=(m-cx)/a
• cx=m-ab
• c=(m-ab)/x
• x=(m-ab)/c

 

this one is the most promising and noted in original description

• y = (ab+cx)/(a+x)
• This will solve for x and draw a vertical line on a graphing calculator at that number if you plug in the variables as so:
• 10.5=(1300+10x)/(100+x)

 

When we can solve for x, I will most likely incorperate this into an xcell sheet. I have not been in an advanced math class in about five years and am struggling at this point. Please help!

Answer 1

if 10.5 = (1300+10x)/(100+x) then 10.5(100+x) = (1300+10x) = 1050+10.5x

Collecting terms, we have 10.5x-10x = 1300-1050 = 250 = .5x Therefore, x =500

check: 10.5 = (1300+5000)/(100+500) = 6300/600 = 10.5 YES