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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

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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.

This problem has been solved

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