Order of Operations

[Property Analysis]

I am attempting to rearrange the equation below so that instead of solving for ROI it will solve for OP. I have successfully solved for ROI using excel equations but I am having difficulty accurately computing the OP value when entering a set ROI and would greatly appreciate any help!

 

[AvgStudent]

I am attempting to rearrange the equation below so that instead of solving for ROI it will solve for OP. I have successfully solved for ROI using excel equations but I am having difficulty accurately computing the OP value when entering a set ROI and would greatly appreciate any help!

View attachment 33466

$$ROI = \frac{(GOI-(TX+INS+W))-(DS*12)}{(OP*DPP)+(OP*CCP)}\\ ROI = \frac{(GOI-(TX+INS+W))-(DS*12)}{OP*(DPP+CCP)}\\ OP = \frac{(GOI-(TX+INS+W))-(DS*12)}{ROI*(DPP+CCP)}\\$$

 

[Dr.Peterson]

$$ROI = \frac{(GOI-(TX+INS+W))-(DS*12)}{(OP*DPP)+(OP*CCP)}\\ ROI = \frac{(GOI-(TX+INS+W))-(DS*12)}{OP*(DPP+CCP)}\\ OP = \frac{(GOI-(TX+INS+W))-(DS*12)}{ROI*(DPP+CCP)}\\$$

I think you're missing the fact that the equation for DS contains OP, so that ROI depends on OP both directly and through DS. What @Property Analysis has done is to replace DS with its expression, so that now he has to solve his third equation for OP.

I am attempting to rearrange the equation below so that instead of solving for ROI it will solve for OP. I have successfully solved for ROI using excel equations but I am having difficulty accurately computing the OP value when entering a set ROI and would greatly appreciate any help!

View attachment 33466

The first thing I notice is that DS is really

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so we can make the work simpler by defining that big fraction to be, say, X. So we have $$DS=OP\cdot X$$
Then the first equation just becomes $$ROI = \frac{(GOI-(TX+INS+W))-(OP\cdot 12X)}{(OP\cdot DPP)+(OP\cdot CCP)}$$
The next step will be to multiply both sides by the denominator, and then collect terms with OP on one side. Can you do the rest?