Question 116306
1). Mario wrote two unit fractions on his paper. (A unit fraction has one as its numerator). The denominators of the fractions are consecutive even integers. If the sum of the fractions is 7/24, what are the two fractional numbers?
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EQUATIONS:
1/2x + 1/(2x+2) = 7/24
Multiply thru by 24x(x+1) to get:
12(x+1) + 12x = 7x(x+1)
12x+12 + 12x = 7x^2+7x
7x^2-17x-12 = 0
x = [17 +- sqrt(625)]/14
x = [17 +- 25]/14
x = 3 or x = -4/7
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1/2x = 1/6 (1st fractional number)
1/(2x+2) = 1/8 (2nd fractional number)
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2). The sum of a number and 20 times its reciprocal is 9. Find the number. 
EQUATION:
x +20(1/x) = 9
x^2 + 20 = 9x
x^2-9x+20 = 0
(x-4)(x-5) = 0
x = 4 or x = 5
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Cheers,
Stan H.