If the numerator of a fraction is increased by 50% and the denominator of the fraction is decreased by 30%, the resultant fraction is 75/49. What is the original fraction?a.5/7b.15/7c.11/17d.5/14
Question
If the numerator of a fraction is increased by 50% and the denominator of the fraction is decreased by 30%, the resultant fraction is 75/49. What is the original fraction?a.5/7b.15/7c.11/17d.5/14
Solution
Let's denote the original fraction as x/y.
According to the problem, if the numerator of the fraction is increased by 50%, it becomes 1.5x. If the denominator of the fraction is decreased by 30%, it becomes 0.7y.
The problem states that the resultant fraction is 75/49. So, we can set up the equation:
1.5x / 0.7y = 75/49
Solving this equation will give us the original fraction x/y.
First, simplify the equation:
1.5x / 0.7y = 75/49
Multiply both sides by 0.7y:
1.5x = 0.7y * 75/49
Simplify the right side:
1.5x = 1.07142857143y
Divide both sides by 1.5:
x = 0.71428571429y
So, the original fraction x/y is approximately 0.71428571429.
Looking at the answer choices, the fraction that is closest to this value is 5/7, which is approximately 0.71428571429.
So, the original fraction is 5/7. The answer is (a) 5/7.
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