I want to achieve a certain Return on Investment (ROI) based on my purchase price, AFTER fixed fees and commission and am trying to calculate the correct **Selling Price:**

Item Cost: £5

**Fixed Sale Fee:** £2

**Commission Fee on Sale Price:** 10%

So, if I sold the item for £15, this is the calculation for profit:

£15 Sell - £5 Cost - £2 Fixed - £1.50 Perc = £6.50 (30% ROI)

I'm trying to backwards engineer this, to find out what my sell price should be, based on a given ROI. For example:

**?? Sell - Cost - Fixed - (% of Sell) = 30% ROI **

How can I work out what the Sell should be?

Start by using what they've been teaching you in class (and what you learned back in middle- and high-school, about pre-algebra percents and beginning-algebra linear equations).

I will guess that you are being tasked with finding a formula which will relate

*any* "item cost" to the required selling price; that is, I'm assuming that "item cost: five pounds" is just an example.

i. You will have an item's wholesale cost. You don't yet know this cost. What variable have you picked for this unknown? (

__variables__)

ii. You need to find the selling price. You don't know the selling price. What variable have you picked for this unknown?

iii. You know that the commission will be ten percent of this (currently unknown) selling price. What expression represents this commission? (

__translating word problems__,

__"percent of" word problems__)

iv. You have a variable for the wholesale cost of the item and you know the fixed selling fee. You now have an expression for the variable commission fee. What expression represents your total costs?

v. You know that you want your return on investment to be thirty percent of the wholesale cost. What expression represents this amount?

vi. This return on investment will be what is left of the selling price, after all costs are deducted. What expression represents this "how much is left" relationship?

vii. What equation can you form? Where does this lead?

If you get stuck, please reply showing your work in following the above step-by-step instructions. Thank you!