Wednesday, October 7, 2009

Number Problem 7 Solution

This is the solution to the algebra number word problem 7 which asked "If the Numerator and Denominator of a certain fraction are both increased by 3, the resulting fraction equals 2/3. If the Numerator and Denominator are both decreased by 2, the resulting fraction equals 1/2. Determine the fraction."

Ok so you have 2 unknowns --> x the numerator and y the denominator. You can solve 2 unknowns with 2 equations. They give you 2 equations.

(x+3)/(y+3) = 2/3 and

(x-2)/(y-2) = 1/2

take the (x+3)/(y+3) = 2/3 and cross multiply and get:

2(y+3) = 3(x+3) which is

2y + 6 = 3x + 9

Now take the second equation: (x-2)/(y-2) = 1/2 and cross multiply
2(x-2) = 1(y-2) which makes

2x - 4 = y - 2 now solve for y
y = 2x - 2

ok now plug this back into the 1st equation for y which we broke down to :
2y + 6 = 3x + 9 so you get 2(2x-2) + 6 = 3x + 9 solve for x

4x - 4 + 6 = 3x+ 9
x= 7 ok now plug 7 into y = 2x - 2 and get y = 2(7) -2 = 12

so the numerator is 7 and the denominator is 12 = 7/12

to check add 3 to the top and bottom and get 10/15 = 2/3

and subtract 2 from the top and bottom and get 5/10 = 1/2







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