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 }. Question from Lorraine, a student: If the numerator of a certain fraction is doubled and the denominator is increased by 1, the fraction becomes 1/2. If the numerator of the original faction is squared and the denominator is decreased by 2, the fraction becomes equal to 1. Let x be the numerator and let y be the denominator of the original fraction. Write down two simultaneous equation in x and y. Solve these equations to find two possible values for the given fraction.

Hi Lorraine,

The original fraction is $\large \frac{x}{y}.$ Look at the second sentence.

If the numerator of the original faction is squared and the denominator is decreased by 2, the fraction becomes equal to 1.

The numerator of the new fraction is the square of the original numerator and the denominator is 2 less than the original denominator. This new fraction is equal to 1 so the numerator and denominator are equal. This gives you one of the two simultaneous equations.

The first sentence tells you how to manipulate the original equation to obtain one with a value of $\large \frac1{2},$ that is a fraction where the denominator is twice the numerator. This gives you a second simultaneous equation.

Make sure you verify your answer.

Penny

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