I suspect that the problem should read as follows:
sukhman wrote:Sam sold his bag at a loss of 6%. Had he sold it for $42 MORE he would have made a profit of 8%. What was the cost price of the bag, in dollars?
a) 300 b) 250 c) 200 d) 150 e)100
We can PLUG IN THE ANSWERS, which represent the cost price of the bag.
When the correct answer choice is plugged in, the difference between an 8% profit and a 6% loss will be $42.
B: 250
8% profit = 8% of 250 = 20.
6% loss = -6% of 250 = -15.
Difference = 20 - (-15) = 40.
Eliminate B.
For the difference to INCREASE, the cost price must be GREATER.
The correct answer is
A.
A: 300
8% profit = 8% of 300 = 24.
6% loss = -6% of 300 = -$18.
Difference = 24 - (-18) = 42.
Success!
Algebraic solution:
Let x = the cost price.
8% profit = (8/100)x.
6% loss = (-6/100)x.
Since the difference between the profit and loss is $42, we get:
(8/100)x - (-6/100)x = 42
(8/100)x + (6/100)x = 42
8x + 6x = 4200
14x = 4200
x = 300.
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