SOLUTION: Good evening ma'am or sir. Will you please help me on how to find the solution in this word problems: 1). Mario wrote two unit fractions on his paper. (A unit fraction has one as

Question 116306: Good evening ma'am or sir. Will you please help me on how to find the solution in this word problems:
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?
2). The sum of a number and 20 times its reciprocal is 9. Find the number.
Thank you very much for your generosity ma'am or sir.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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?
----------
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
-------------------
1/2x = 1/6 (1st fractional number)
1/(2x+2) = 1/8 (2nd fractional number)
====================
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
===================
Cheers,
Stan H.

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