The denominator of a fraction is one more than twice its numerator. If the numerator and denominator are both increased by 5, it becomes 3/5. Find the original fraction.
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Let us assume, x is the numerator and y is the denominator of the fraction
Given:
y = 2x + 1
y - 2x = 1----------------1
Also given:
(x + 5) / (y + 5) = 3/5
5 (x + 5) = 3 ( y + 5)
5x + 25 = 3y + 15
3y - 5x = 10 --------------2
Multiply equation 1 by 3
3y - 6x = 3 ----------------3
Subtract equation 3 from equation 2
x = 7
Therefore, y = 2x + 1 = 2 * 7 + 1 = 15
Answer - The original fraction = 7/15
Given:
y = 2x + 1
y - 2x = 1----------------1
Also given:
(x + 5) / (y + 5) = 3/5
5 (x + 5) = 3 ( y + 5)
5x + 25 = 3y + 15
3y - 5x = 10 --------------2
Multiply equation 1 by 3
3y - 6x = 3 ----------------3
Subtract equation 3 from equation 2
x = 7
Therefore, y = 2x + 1 = 2 * 7 + 1 = 15
Answer - The original fraction = 7/15
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