In a fraction ,twice the numerator is2 more than the denominator.if 3 is added to the numerator and to the denominator,the new fraction is 2/3.find the original number
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Let us assume, x is the numerator and y is the denominator of the fraction.
Given:
2x = y + 2
2x - y = 2 ------------------1
Also given:
(x + 3) / (y + 3) = 2/3
3 (x + 3) = 2 (y + 3)
3x + 9 = 2y + 6
2y - 3x = 3 --------------2
Multiply equation 1 by 2
4x - 2y = 4 ----------------3
Adding equation 2 and equation 3
x = 7
substitute, the value of x in a equation 2x = y + 2
2 * 7 = y + 2
y = 14 - 2 = 12
Therefore, the original fraction is 7/12
Given:
2x = y + 2
2x - y = 2 ------------------1
Also given:
(x + 3) / (y + 3) = 2/3
3 (x + 3) = 2 (y + 3)
3x + 9 = 2y + 6
2y - 3x = 3 --------------2
Multiply equation 1 by 2
4x - 2y = 4 ----------------3
Adding equation 2 and equation 3
x = 7
substitute, the value of x in a equation 2x = y + 2
2 * 7 = y + 2
y = 14 - 2 = 12
Therefore, the original fraction is 7/12
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