SOLUTION: The Susan Hansen Group in St. George, Utah, sells $16,000,000 of single-family homes and town homes a year. If single-family homes, with an average selling price of $250,000, sell

Question 1015424: The Susan Hansen Group in St. George, Utah, sells $16,000,000 of single-family homes and town homes a year. If single-family homes, with an average selling price of $250,000, sell 3.5 times more often than town homes, with an average selling price of $190,000, how many of each are sold? (Round to nearest whole.)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x = number of single family homes.
y = number of town homes

250,000 * x + 190,000 * y = 16,000,000

this equation says that x number of single family homes, selling at 250,000 each, plus y number of town homes, selling at 190,000 each, total 16,000,000 in sales.

you are given that single family homes sell 3.5 times as much as town homes.

since x = number of single family homes sold and y = number of town homes sold, then your equation becomes:

x = 3.5 * y.

that equation says that the number of single family homes sold is 3.5 times the number of town homes sold.

in the equation of 250,000 * x + 199,000 * y = 16,000,000, replace x with 3.5 * y to get:

250,000 * x + 190,000 * y = 16,000,000 becomes:

250,000 * 3.5 * y + 190,000 * y = 16,000,000.

simplify to get 875,000 * y + 190,000 * y = 16,000,000.

combine like terms to get 1,065,000 * y = 16,000,000.

divide both sides of this equation to get y = 16,000,000/1,065,000 = 15.02347418.

since x = 3.5 * y, then y = 52.58215962.

they sold 15.02347418 town homes and 52.58215962 single family homes.

15.02347418 * 190,000 + 52.58215962 * 250,000 = 16,000,000.

round off to the nearest integer and you get:

15 town homes were sold and 53 single family homes were sold.

15 * 190,000 + 53 * 250,000 = 16,235,000 total dollars in sales.

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