Exercise 1:

If we multiply the numerator of a fraction by three and add 12 to the denominator, the value of the fraction becomes three-quarters. If the numerator is increased by 7 and the denominator is tripled, the value of the fraction changes. Find the fraction.

x - nominator y - denominator
y + 12 3 x ​ = 4 3 ​ 3 y x + 7 ​ = 2 1 ​ 3 ( y + 12 ) = 12 x 2 ( x + 7 ) = 3 y 3 y + 36 = 12 x 2 x + 14 = 3 y 2 x + 14 + 36 = 12 x 10 x = 50 x = 5 3 y = 2 ⋅ 5 + 14 3 y = 10 + 14 3 y = 24 y = 8 y x ​ = 8 5 ​ ​

Answered by konrad509 | 2024-06-10

The fraction is 8 5 ​ . This was determined by setting up equations based on the conditions given in the problem and solving for the numerator and denominator. Verification shows that the fraction meets both initial conditions provided in the question.
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Answered by konrad509 | 2024-12-24