Question

A fraction becomes

1/3, if 2 is added to both of its numerator and denominator. If 3 is added to both of its numerator and denominator then it becomes

2/5.Form a linear equation to represent it.​

Answer 1

Answer:

3x - y = - 4

5x - 2y = - 9            , moreover

  fraction = x/y = 1/7

Step-by-step explanation:

Let the numerator be 'x' and denominator be 'y'. Thus, fraction be x/y.

if 2 is added to both of its numerator and denominator, fraction becomes 1/3:

⇒ (x + 2)/(y + 2) = 1/3

⇒ 3(x + 2) = y + 2

⇒ 3x - y = - 4        ...(1)

If 3 is added to both of its numerator and denominator then it becomes  2/5.

⇒ (x + 3)/(y + 3) = 2/5

⇒ 5(x + 3) = 2(y + 3)

⇒ 5x - 2y = - 9       ...(2)

These two equations(linear) represent the given conditions, where x is numerator and y is denominator.

from (1), y = 3x + 4,   substitute in (2):

=> 5x - 2y = - 9       ⇒ 5x - 2(3x+4) = -9

=> x = 1        and thus y = 3(1) + 4 = 7

Answer 2

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Let Numerator = x

Let denominator = y

1/3, if 2 is added to both of its numerator and denominator.

$\: \frac{x + 2}{y + 2} = \frac{1}{3}$

now, apply cross multiplication

$3(x + 2) = y + 2 \\ 3x + 6 = y + 2 \\ 3x = y + 2 - 6 \\ 3x = y - 4 \\ 3x - y = - 4$

Now, substitute it

y = 3x+4

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Now, If 3 is added to both of its numerator and denominator then it becomes 2/5.

$\frac{x + 3}{y + 3} = \frac{2}{5}$

now, apply cross multiplication

$5(x + 3) = 2(y + 3) \\ 5x + 15 = 2y + 6 \\ 5x - 2y = 6 - 15 \\ 5x - 2y = - 9$

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Now, form a linear equation to represent it

• y = 3x+4
• 5x-2(3x+4)-9

x = 1

So, y= 3(1)+4= 7

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hope it helps❤᭄࿐