Answer:
The value of the house on 1st January 2015 was of $650,000.
Step-by-step explanation:
Decimal multipliers:
For a increase of a%, the decimal multiplier is given by [tex]\frac{100+a}{100}[/tex]
For a decrease of a%, the decimal multiplier is given by [tex]\frac{100-a}{100}[/tex]
Rami bought a house on 1st January 2015.
For a value of x.
In 2015 the house increased in value by 15%.
This means that x is multiplied by [tex]\frac{100+15}{100} = \frac{115}{100} = 1.15[/tex]
In 2016 the house decreased in value by 8%.
This means that 1.15 times x is multiplied by [tex]\frac{100-8}{100} = \frac{92}{100} = 0.92[/tex]
On 1st January 2017 the value of the house was $687700.
The value of these multiplications is 687700.
What was the value of the house on 1st January 2015?
This is x, so:
[tex]x*1.15*0.92 = 687700[/tex]
[tex]x = \frac{687700}{1.15*0.92}[/tex]
[tex]x = 650000[/tex]
The value of the house on 1st January 2015 was of $650,000.
