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A positive integer is 3 less than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is 9/20, then find the two intege

find both integers

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Lauren H. | Experienced High School Chemistry TeacherExperienced High School Chemistry Teache...
4.8 4.8 (12 lesson ratings) (12)
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x + 3 = y
 
1/x + 2/y = 9/20
 
Substitute
 
1/x + 2/x+3 = 9/20
 
Multiply by 20
 
20/x + 40/x + 3 = 9
 
Multiply by x
 
20 + 40x/x + 3 = 9x
 
Multiply by x + 3
 
20(x + 3) + 40 x = 9x(x + 3)
 
20x + 60 + 40x = 9x^2 + 27x
 
9x^2 - 33x - 60 = 0
 
divide by 3
 
3x^2 + 11x - 20 = 0
 
Factor
 
(3x + 4) ( x - 5) =0
 
Integer must be positive, so x = 5 and y = 8