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in Linear Equations by (58.8k points)

The denominator of a rational number is greater than its numerator by 7. If the numerator is increased by 17 and the denominator decreased by 6, the new number becomes 2. Find the original number.

1 Answer

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Best answer

Let the rational number be x/y

According to the question we can write as y=x+7

Which implies x=y-7 and (x+17)/(y-6) = 2

Now substituting the value of x in above equation we get

(y-7+17)/(y-6) = 2

Now by rearranging,

(y-7+17)=2(y-6)

y+10=2y-12

y=22

But x=y-7=22-7=15

So the number is 15/22

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