Question

A fraction becomes 4/5 , if 2 is added to both numerator and denominator. However, if 4 is subtracted from both numerator and denominator, then the fraction becomes 1/2 Represent this situation algebraically and solve graphically.

pls help​

Answer 1

Answer:

6/8

Step-by-step explanation:

Let fraction be x/y

Now x+2/y+2=4/5

=>5x+10=4y+8

=>5x+2=4y....EQ1

x-4/y-4=1/2

=>2x-8=y-4

=>2x-4=y...EQ2

From EQ1 and EQ2

x=6, y=8

Answer 2

Given: A fraction becomes 4/5 , if 2 is added to both numerator and denominator. However, if 4 is subtracted from both numerator and denominator, then the fraction becomes 1/2.

To find: The original fraction

Solution: Let the fraction be x/y. Here, x is the numerator and y is the denominator.

Now, when 2 is added to both x and y, the fraction becomes 4/5. Therefore,

$\frac{x + 2}{y + 2} = \frac{4}{5}$

=> 5(x+2) = 4(y+2)

=> 5x+10 = 4y+8

=> 5x-4y = 8-10

=> 5x-4y= -2 -----equation (i)

When 4 is subtracted from both x and y, the fraction becomes 1/2. Therefore,

$\frac{x - 4}{y - 4} = \frac{1}{2}$

=> 2(x-4) = y-4

=> 2x-8 = y -4

=> 2x-y = -4+8

=> 2x-y= 4 -------equation(ii)

Plotting these two lines on graph, the x-coordinate and y-coordinate of intersection of the lines gives the value of x and y respectively.

The attached graph clearly shows that the lines intersect at (6,8). Therefore,

Value of x = 6

Value of y= 8

Therefore, the original fraction is 6/8.