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if the numberatior of a fraction is increased by 4 and the demominatio is decreased by 3 then the fraction becomes 2/3 and if both numberator and demonitor are increade by 5 then the fraction becomes 1/2 the orignal fraction is

User Neworld
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1 Answer

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The original fraction is
(8)/(21).

Let the numerator be represented by x, and the denominator by y. So that;


(x + 4)/(y - 3) =
(2)/(3) ............... 1


(x + 5)/(y + 5) =
(1)/(2) ............ 2

From equation 1, we have;

2y - 6 = 3x +12

2y - 3x = 6 + 12

3x - 2y = -18.......................... 3

From equation 2, we have;

2x + 10 = y + 5

2x - y = -10 + 5

2x - y = -5 ....................... 4

Multiply equation 3 by 2, and equation 4 by 3 to have;

6x - 4y = -36 ........... 5

6x - 3y = - 15 ............. 6

subtract equation 6 from 5,

6x - 6x -4y + 3y = -36 + 15

-y = -21

y = 21

Substitute the value of y in equation 4,

2x - y = -5

2x - 21 = -5

2x = -5 + 21

2x = 16

x = 8

Thus, the original fraction is
(8)/(21).

User Neebz
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