backwards gross profit

K

kelsie882

New member
Joined
Aug 5, 2019
Messages
5
I'm trying to figure out how much I need to charge for an item. I know how much I want my gross profit to be, but how to do I figure my list price with fees?

Ex:

I want my gross profit on Item A to be $250.
There is a fee of 5% on only the list price of Item A.
There is another fee of 3% + $.25 on only the list price of Item A.
There is a cost of $9 associated with Item A.

What does my list price need to be to gross $250??
 
[MATH]p = \text {list price in dollars.}[/MATH]
[MATH]p - 0.05p - (0.03p + 0.25) - 9 = 250 \implies[/MATH]
[MATH]0.92p = 259.25 \implies p = \dfrac{259.25}{0.92} \approx 281.79 \text { dollars.}[/MATH]
5% fee is 14.09. 3% fee plus a quarter is 8.70. 14.09 + 8.70 + 9.00 = 31.79.

281.79 - 31.79 = 250.
 
Thank you!!! That's exactly what I was looking for! I tried working it backwards like that but my math was off...
 
JeffM said:
[MATH]p = \text {list price in dollars.}[/MATH]
[MATH]p - 0.05p - (0.03p + 0.25) - 9 = 250 \implies[/MATH]
[MATH]0.92p = 259.25 \implies p = \dfrac{259.25}{0.92} \approx 281.79 \text { dollars.}[/MATH]
5% fee is 14.09. 3% fee plus a quarter is 8.70. 14.09 + 8.70 + 9.00 = 31.79.

281.79 - 31.79 = 250.
Click to expand...

ok I lied. This makes no sense the longer I look at it. I’d like to be able to figure this out for any value and I can’t seem to. Any help would be much appreciated.
 
Can you show us your work with the other example with different values so we can see where you are wrong?
 
Jomo said:
Can you show us your work with the other example with different values so we can see where you are wrong?
Click to expand...


I don't understand where the .92p came from? From what I remember from high school algebra, whatever you do to one side of the equation you do to the other; and you can combine like terms. Aren't .05p and .03p like terms? Doesn't that make it .08p? then you divide p and 250 by .08?
 
I think you missed the [MATH]p[/MATH] by itself.

Expand the parentheses in the equation [MATH]p - 0.05p - (0.03p + 0.25) - 9 = 250[/MATH] step by step, and then combine like terms. Probably you are trying to do this too fast, writing too little.

As was requested, please show your detailed work, so we can see where you are going wrong specifically.
 
kelsie882 said:
I don't understand where the .92p came from? From what I remember from high school algebra, whatever you do to one side of the equation you do to the other; and you can combine like terms. Aren't .05p and .03p like terms? Doesn't that make it .08p? then you divide p and 250 by .08?
Click to expand...
Yes, [MATH]-\ 0.05p[/MATH] and [MATH]-\ 0.03p[/MATH] are like terms.

Yes, [MATH]-\ 0.05p - 0.03p = -\ 0.06p.[/MATH]
But you are not done combining like terms.

[MATH]p - 0.08p = p(1 - 0.08) = 0.92p.[/MATH]
Furthermore you ignored the 9.00 cost and the 0.25 fee. So you do not divide anything into 250.

As for its not making sense, remember that I actually worked it out arithmetically for you to show why it makes sense.

[MATH]5\% \text { of } 281.79 = 14.0895 = 14.09 \text { rounded.}[/MATH]
[MATH]3\% \text { of } 281.79 = 8.4537 = 8.45 \text { rounded.}[/MATH]
[MATH]8.45 + 0.25 = 8.70.[/MATH]
[MATH]281.79 - 14.09 - 8.70 - 9.00 = 250[/MATH] is the arithmetic version of

[MATH]p - 0.05p - (0.03p + 0.25) - 9.00 = 250.00.[/MATH]
 
p-.05p-(.03p+.25)-9=250
+9=+9

p-.05p-(.03p+.25)=259
-.25 =258.75

p-.08p=258.75
\.08=\.08

p=32.34

Is how I would solve the above equation. I'm sure it's wrong. It's been 17 years since freshman algebra and contrary to what my teachers told me, I never use it so I don't remember how.

HOWEVER...it lead to me figure out that If I add $9 to my value; $250 = $259 and then divide that by .08*100 and add that to the $259 it give me apprx $292; which after 8% and subtracting $9 will give apprx $250.
 
kelsie882 said:
p-.05p-(.03p+.25)-9=250
+9=+9

p-.05p-(.03p+.25)=259
-.25 =258.75

p-.08p=258.75
\.08=\.08

p=32.34

Is how I would solve the above equation. I'm sure it's wrong. It's been 17 years since freshman algebra and contrary to what my teachers told me, I never use it so I don't remember how.

HOWEVER...it lead to me figure out that If I add $9 to my value; $250 = $259 and then divide that by .08*100 and add that to the $259 it give me apprx $292; which after 8% and subtracting $9 will give apprx $250.
Click to expand...
You have a few mistakes.
p-.08p=258.75
\.08=\.08

p=32.34
You did divide the rhs by .08 correctly but did a terrible job on the lhs. First of all .08/.08 is not 0, but rather it is 1. Where is your 1? Also you divided the whole rhs by .08 but only part of the lhs by .08. It seems that you divided only .08 by .08. What about the p, it should also be divided by .08. Your main mistake here is that you did not combine like terms. What is p-.08p after you combine the like terms?

p-.05p-(.03p+.25)=259
-.25 =258.75
p-.08p=258.75
My first comment is that you know as well as I do that -.25 does NOT equal 258.75 yet you wrote that. Why would you write that!!?
It seems that you subtracted .25 from both sides. You got the correct result on the rhs. The lhs is not correct. The lhs originally had -.25. So if you then subtracted .25 you should get -.50 not 0. Maybe adding .25 to both sides would be a better idea.
 
You must log in or register to reply here.
Top