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Some office workers bought a $60 gift for their boss. If there have been 5 more employees to contribute, everyone's cost would have been $2 less. How many workers contributed to the gift?



Answer :

crisforp
x * y = 60;
( x + 5 ) * ( y - 2 ) = 60 => xy + 5y - 2x - 10 = 60 => 5y - 2x = 10 =>
x = ( 5y - 10 ) / 2;

But x * y = 60 => [ ( 5y - 10 ) / 2] * y= 60 => 5y^2 - 10y - 120 = 0 ;
The discriminant is 2500 => y1 = ( 10 + 50 ) / 10 => y1 =$ 6 > 0 ( okay );
y2 = ( 10 - 5 0 ) / 10 => y2 = - 4 < 0 ( isn't okay );

Then x = ( 30 - 10 ) / 2 => x = 10 workers contributed to the gift .,

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