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Question 285517: Hello! I'd greatly appreciate it if anyone can help me on this deceptively hard (for me, at least) word problem. It is as follows:
A storeowner's average day sales is $500, realizing a profit of 20% of the selling price. To increase the volume of his sale, he advertised his goods by spending an average of $20 a day for advertising. If his average daily sales rose to $700 with the rate of the profit still remaining the same, how much additional profit did the advertising bring?
Thank you very much for the time and help! Godspeed! :)
Found 2 solutions by vleith, Greenfinch:
Answer by vleith(2983)   (Show Source):
You can put this solution on YOUR website! First let's find how much profit the owner was making at the beginning. "A storeowner's average day sales is $500, realizing a profit of 20% of the selling price."
 He was making $100 a day in profits.
"he advertised his goods by spending an average of $20 a day for advertising."
So we know that whatever his daily sales become, he must add $20 to his daily costs.
"If his average daily sales rose to $700 with the rate of the profit still remaining the same, ..."
So the storeowner's sales went up by 40%. He now sees $140 a day, but his costs went up by $20 in advertising. He must deduct that $20 from his profits.
"how much additional profit did the advertising bring?"
Let's look at that another way.
The original sales of $500 resulted in profits of $20. Let's say, for fun, that he sold 5 items worth $100 each. If that were the case, the owner makes $20 on each sale.
Now, he advertises and sells 7 items. Each item would also add $20. So 2 more sales means $40.
But, he spends an additional $20 advertising to get those two extra sales. So he nets 40 - 20 = $20 in 'real profit'.
If the owner was only able to sell 6 units instead of 7 ($600 in sales), then his revenue would increase but his profit would stay the same.
If the owner sold more than $500 and less than $600, his sales would go up, but his profit would decline. It is not easy being a shopowner.
Answer by Greenfinch(383)  (Show Source):
You can put this solution on YOUR website! The wording is what makes it hard. Why cannot Mathematicians consider learning English!
Initially, the sales are $500 from which there is a profit of $100
Afterwards there are sales of $700, from which there is a profit of $140.
Assuming that the advertising is an extra cost of $20, the extra profit is $20 less than the $140 - $100 difference, or $20.
If however, the rate of profit stays the same, this might be construed to mean that the advertising is now included in the costs of sales and does not have to be considered seperately. In that case the profit increase is $40 per day.
Either interpretation is possible when the question is written in this way.
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