solve word problem using algebra

Question

The Susan Hansen group in st. george, utah, sells $16,000,000 of single-family homes and townhomes a year. if a single family home, with an average selling price of 250,000, sell 3.5 times more often than townhomes, with an average selling price of $190,000, how many of each are sold? Round to the nearest whole.

Answer 1

Let X be the number of townhomes sold at $190,000

Then 3.5*X is the number of single family homes sold at $250,000  

 

The total sales are $16,000,000 so  

 

190,000*X + 250,000*3.5*X = 16,000,000  

190*X + 250*3.5*X = 16000  

190*X + 875*X = 16000

1065*X = 16000

X = 15.02 ~ 15 

 

3.5*X = 52.6 ~ 53 

 

So there are 15 townhomes and 53 single family homes sold a year 

 

Check:  15*190,000 + 53*250,000 = 2,850,000 + 13,250,200 = 16,100,000 ~ $16,000,000