A merchant decides to sell off 100 articles a week at a selling price

Question

A merchant decides to sell off 100 articles a week at a selling price of $150 each. For each 4% rise in the selling price he sells 3 less articles a week. If the selling price of each article is $x, where x > 150, then which of the below expression represents the amount in dollars, the merchant will receive from the sales of the articles in a week ?

A. 175 - x/2
B. x/3 + 156
C. 350 - x^2/2
D. x^2 - 2x + 75
E. x^2 + 2x + 75

A. 175 - x/2
B. x/3 + 156
C. 350 - x^2/2
D. x^2 - 2x + 75
E. x^2 + 2x + 75

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IanStewart · Answer

I'm either not understanding the question correctly, or there is a problem with it. When the price is $150, the merchant makes $15,000. If he raises the price slightly he will make roughly that amount, so D and E are the only reasonable answers (A, B and C are far too small). But we can see that if he raises the price 4%, to $156, he will sell 97 items. His revenue will be 156*97 dollars. That's an even number, but answers D and E will both be odd numbers if you plug in x = 156. So none of the answer choices could be right.

It's unclear to me exactly what the question is asking, because it's not clear if the percent increase described is meant to compound. Assuming it is not, then since 4% of $150 is $6, when the price increases by $6, the vendor sells 3 fewer items.

We're told the price is $x. The number of items sold will be 100 - 3*(x - 150)/6 = 100 - (x-150)/2 = 175 - (x/2).

Multiplying number of items by price, we get revenue:

x(175 - x/2) = 175x - x^2/2

so that should be the answer, unless I've misunderstood what the question is trying to say.

Note also that if the sales drop by 3 for every $6 increase in price, so drop by 1 for every $2 increase in price, we should expect the revenue to be $0 when the price is $350 (because if the price rises by $200, sales drop by 100, so sales drop to zero). So we should expect something like (350 - x) or (175 - x/2) to be a factor of the correct answer here, a fact one might be able to use to avoid doing all the work above.

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A merchant decides to sell off 100 articles a week at a selling price

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