SOLUTION: The Susan Hansen Group in St. George, Utah, sells $16,000,000 of single-family homes and townhomes a year. Assume single-family homes, with an average selling price of $260,000, se

Question 1196779: The Susan Hansen Group in St. George, Utah, sells $16,000,000 of single-family homes and townhomes a year. Assume single-family homes, with an average selling price of $260,000, sell 1.5 times more often than townhomes, with an average selling price of $230,000. How many of each are sold?
Found 3 solutions by math_tutor2020, greenestamps, ikleyn:
Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

x = number of townhomes
1.5x = number of single-family homes since they sell 1.5 times more often compared to townhomes

230,000x = amount of money made from selling the townhomes
260,000*1.5x = 390,000x = amount of money made from selling the single-family homes

The two subtotals add to $16,000,000
230,000x+390,000x = 16,000,000
(230,000+390,000)x = 16,000,000
620,000x = 16,000,000
x = (16,000,000)/(620,000)
x = 25.806 approximately

The fact we don't get a whole number for x seems to suggest that there might be a typo in one (or more) of the numbers in the question.
I would ask your teacher for further clarification.

Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!

"1.5 times MORE often" means 2.5 times AS OFTEN. It's the same as an increase of 150% meaning the new number is 250% of the original.

Using that (and working in thousands of dollars)....

x = # of townhomes
2.5x = # of single-family homes

....

We still don't get an integer answer....

So, regardless of whether the "1.5 times more often" is (wrongly) interpreted as meaning 1.5 times AS often, or is interpreted correctly as 2.5 times as often, the given information is faulty.

That's pretty sad. Usually, when a problem uses a phrase like "1.5 times as often" or "3 times more than", only one of the two interpretations yields an integer answer, giving an indication of what the author of the problem really meant.

But in this case neither interpretation gives a valid answer.

Answer by ikleyn(52777)   (Show Source): You can put this solution on YOUR website!
.

                Will consider this problem as " dead from the moment of creation ".

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