the product of a girl age five years ago and 8 years from now is 30.find her present age.
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Present age of girl is 7 years
Explanation:
Let the present age of girl be ' x ' years
Age of girl 5 years ago = ( x - 5 ) years
Age of girl 8 years from now = ( x + 8 ) years
Product = 30
=> ( x - 5 )( x + 8 ) = 30
=> x(x + 8) - 5( x + 8 ) = 30
=> x² + 8x - 5x - 40 = 30
=> x² + 3x - 40 = 30
=> x² + 3x - 40 - 30 = 0
=> x² + 3x - 70= 0
=> x² + 10x - 7x - 70 = 0
=> x(x + 10) - 7(x + 10) = 0
=> (x + 10)(x - 7) = 0
=> x + 10 = 0 or x - 7 = 0
=> x = - 10 or x = 7
But x = - 7 is neglected since ages cannot be negative
=> x = 7
Therefore the present age of girl is 7 years
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