Question

Exercise

1. If we multiply by three the numerator of a fraction and add 12 to the denominator, the value of the fraction is three quarters, and if the numerator increases in 7 and the denominator trebles the value of the fraction is a way, finds the fraction.

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Answer 1

x - nominator
y - denominator


`(3x)/(y+12)=(3)/(4)\\ (x+7)/(3y)=(1)/(2)\\\\ 3(y+12)=12x\\ 2(x+7)=3y\\\\ 3y+36=12x\\ 2x+14=3y\\\\ 2x+14+36=12x\\ 10x=50\\ x=5\\\\ 3y=2\cdot5+14\\ 3y=10+14\\ 3y=24\\ y=8\\\\ (x)/(y)=\boxed{(5)/(8)}`