MHB Calculate Selling Price for Cucumbers inc. VAT (42% Profit Margin)

[LizQUIZE]

The grocery stores goal profit margin is 42% from selling price apart from the wastage. What is the selling price for the cucumbers including VAT when the purchase price (without VAT) is 1,30$ and about 90 % are sold from the purchased cucumbers? The VAT for food is 14 % year 2016.I do not know where to start with this one.

 

[HallsofIvy]

Suppose n cucumbers are bought for 1,30 the total cost is 1,30n. Let the selling price be p. If, because of wastage, on 90% of those cucumber, 0,9n, can be sold, you will bring in 0,9np. Your "value added" will be (0,9np- 1,30n)= (0,9p- 1,30)n so VAT will be 0,14(0,9- 1,30)n. You want to make a profit of 42% of the selling price so you want 0,9np- 0,14(0,9- 1,30)n- 1,30n= 0.42n. Divide through by n to get 0,9p- 0,14(0,9p- 1,3)= 0,42. Solve that equation for p.
(I had to drop all currency signs because they were interpreted as delimiters.)
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