Question 1207346: Amana owns two houses in the same community. The ratio of the values of the first to the second house is 10: 15 respectively. It is estimated that in 6 years, the value of the first house will increase by 35% and that of the second house will increase by $30,825.00. If the new ratio is 3: 4, find the original value of the first house.
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! Amana owns two houses in the same community. The ratio of the values of the first to the second house is 10: 15 respectively. It is estimated that in 6 years, the value of the first house will increase by 35% and that of the second house will increase by $30,825.00. If the new ratio is 3: 4, find the original value of the first house.
The ratio of the values of the first to the second house is 10: 15 respectively.
Let the common multiple be x
Values of the first house will be 10x
the value of second house will be 15x
Value of the first house after 6 years will be 1.35* 10x
Value of the second house after 6 years will be 15x +30825.00
Now the ratio is 3:4
(1.35* 10x)/(15x +30825.00) =3/4
13.5x /(15x +30825.00)= 3/4
4* 13.5x = 3*(15x +30825.00)
54x = 45x +92475
9x = 92475
x =10275
Value of first house = 10x = 102,750
Value of second house = 15x = 154125
CHECK
(102750+ (1.35*10275))/(154125+30) =0.756
The original value of the first house is $ 102,750.00
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