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Question 1054184: The ratio of the price of two house is 16:23.two years later the price of the first had raised by 10% and that of the second by $477.the ratio of the price became 11:20.find the original prices of the houses.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let a equal the price of the first home.
let b equal the price of the second home.
the ratio of the price of the first home to the price of the second home is equal to 16/23.
this means that the price of the first home divided by the price of the second home is equal to 16/23.
you have:
a/b = 16/23
after 2 years the price of the first home has increased to 1.1 times its original amount.
after 2 years the price of the second home has increased by 477 dollars.
after 2 years, the ratio of the first home to the price of the second home is equal to 11/20.
this means that the price of the first home divided by the price of the second home has become 11/20.
you have:
(1.1 * a) / (b + 477) = 11/20
you have 2 equations that need to be solved simultaneously.
they are:
a/b = 16/23
(1.1 * a) / (b + 477) = 11/20
in the first equation, solve for a to get a = 16/23 * b.
in the second equation, replace a with 16/23 * b to get:
(1.1 * 16/23 * b) / (b + 477) = 11 / 20
simplify to get:
17.6 / 23 * b / (b + 477) = 11 / 20
multiply both sides of this equation by 20 to get:
352 / 23 * b / (b + 477) = 11
multiply both sides of this equation by 23 to get:
352 * b / (b + 477) = 253
multiply both sides of this equation by (b + 477) to get:
352 * b = 253 * (b + 477)
simplify to get:
352 * b = 253 * b + 120681
subtract 253 * b from both sides of this equation to get:
352 * b - 253 * b = 120681
simplify to get:
99 * b = 120681
divide both sides of this equation by 99 to get:
b = 120681 / 99 = 1219
since you know that a = 16/23 * b, this means that a = 848.
the price of the first home is currently 848.
the price of the second home is currently 1219
the ratio of the first home to the second home is 848 / 1219 = 16/23
in 2 years, the price of the first home will be 848 * 1.1 = 932.8.
in 2 years, the price of the second home will be 1219 + 477 = 1696.
in 2 years, the ratio of the price of the first home to the price of the second home will be 932.8 / 1696 = 11/20.
numbers look good.
the price of the first home is currently 848.
the price of the second home is currently 1219.
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