# How do I isolate X in X = ((c + d(e / a)) - (eX)) / ab;

I have a real life situation where I must find an average speed (more information below) but I am not good enough at algebra to isolate my variable. Could you please tell me how it's done?

I'm having some variables that I know :

a : Number of hours available per week = 960 hours

b : Target production time = 3.5 weeks

c : Current order book value = $700.000 d : Projected orders per week =$125.000 / week

e : Hours left to reach target production time = 9800 hours

And those I don't know :

X = Target rate of delivery ($/h) Y = Target order book value So then I made these two equations : eq1 : X = Y / ab eq2 : Y = (c + d(e / a)) - (eX) If I eliminate Y i get : eq : X = ((c + d(e / a)) - (eX)) / ab But then I don't know where to start if I want to isolate X. I know very well that the value of X depends on it's own value because the higher the value of X, the higher the value of Y, which will decrease the value of X. I don't know any way to find where this leads. How should I proceed from here? ## 1 Answer As I understand it you want to solve the following equation: $$X = \frac{c + d\frac{e}{a} - eX}{ab}$$ First separate the fraction to obtain $$X = \frac{c + d\frac{e}{a}}{ab}-\frac{eX}{ab}$$ Then add the right hand term to both sides, $$X + \frac{eX}{ab}= \frac{c + d\frac{e}{a}}{ab}$$ Now factor out the$X\$ in the left hand side, $$X\left(1+\frac{e}{ab}\right)=\frac{c+d\frac{e}{a}}{ab}.$$ Now divide through by the bracketed factor, $$X=\frac{\frac{c+d\frac{e}{a}}{ab}}{1+\frac{e}{ab}}.$$ Using algebra of fractions you get the nice form $$X=\frac{a c+d e}{a^2 b+a e}.$$

• Cool! I should have thought about separating the fraction. It's been a long while. Many thanks! May 4, 2017 at 21:08
• You're welcome. Remember to upvote and accept the answer if you found it useful :-) May 4, 2017 at 21:09
• Ps make sure the denominator is never zero. Dividing by zero is nonsensical. Jul 8, 2017 at 22:44