Question 1207784
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x = initial price
0.40x = discount value = amount saved for the customer
x - 0.40x = 0.60x = sale price
0.60x - 20 = profit per shirt = 4 dollars


0.60x - 20 = 4
0.60x = 4+20
0.60x = 24
x = 24/0.60
x = 40
The initial price should be <font color=red>$40</font>.


If that's the case then 40% of $40 = 0.40*40 = 16 dollars is saved and the sale price would be 40-16 = 24 dollars (or 60% of 40 = 0.60*40 = 24).
Then profit per shirt = price-cost = 24-20 = 4 dollars.
We have confirmed $40 is the correct starting price.


Now consider a 50% discount.
The customer saves 0.50*40 = 20 dollars.
The sale price is 40-20 = $20
The profit per shirt is $0 since price-cost = 20-20 = 0.
The manager doesn't gain any money, nor loses money. The manager breaks even.
The old profit $4 dropped to $0, so the profit reduced by <font color=red>$4</font>.


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Summary:


Initial price should be <font color=red>$40</font>
Profit is reduced by <font color=red>$4</font> if you give a 50% discount instead of a 40% discount.
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