Question

Solve the following problems
1. The numerator of a fraction is greater than its denominator by 3. If the
numerator is decreased by 2 and the denominator is increased by 4,
then the new fraction is
3⁄4. Find the original fraction.

Answer 1

Answer:

answer-12/25

Step-by-step explanation:

Let the fraction be

y

x

Then, according to the given conditions, we have

y−3

3x =

11

18 and 2yx+8 = 52

⇒11x−6y−18 and 5x+40=4y

⇒11x−6y+18=0 and 5x−4y+40=0

By cross-multiplication, we have

(−6)×40−(−4)×18x = 11×40−5×18−y=11×(−4)−5×(−6)1

⇒ −240+72x = 440−9−y = −44+301

⇒ −168x = −350y = −141

⇒x= −14−168 and y= −14−350

⇒x=12 and y=25

Hence, the fraction is 12/25

.