If the numerator is increased by 5, and the denominator is decreased by 3, the?

Question

Let x/ y represent a fraction
If the numerator is increased by 5, and the denominator is decreased by 3, the
resulting fraction is 1/4
.
However, if the numerator is decreased by 22/5, and the denominator is tripled,
the resulting fraction is – 2/5. Find the fraction x/y
.

? · Answer

OK. 
 
(x 5)/(y-3) = 1/4  cross multiply to get y in terms of x ===> y = 23 4x. 
 
(x - 22/5)/3y = -2/5  substitute in for y, cross multiply and solve for x  ==> 580 = -145x  
Answer is  x = -4 and y = 7 and fraction is -4/7 
These check.

lenpol7 · Answer

(x +5) / (y + 3)  = 1/4

(x - 22/5) / (3y) = -2/5

This is a form of Simultaneous Equations. 
4(x + 5) = y + 3) 
4x + 20 = y + 3 
4x - y = -17 
First fractions!!!!!

5(x - 22/5) = -2(3y) 
5x - 22 = -6y 
5x + 6y = 22   second fraction ,

Hence 
4x - y = -17    ( multiply by '6') 
5x + 6y = 22

24x - 6y = - 102
5x + 6y = 22 
Add 
29x = - 80 
x = -80/29

4(-80/29) - y = -17 
y = -320/29 + 17 
y = (-320 + 493) / 29 
y = 173/29

Hence x/y = [-80/29]/ [ 173/29] 
x/y = -80 / 29 X 29 / 173 
Cancel down by '29' 
Hence 
x/y = -80/ 173

If the numerator is increased by 5, and the denominator is decreased by 3, the?

2 respuestas