Question

The sum of the numerator and the denominator of a fraction is equal to 7. Four times the numerator is 8 less than 5 times the denominator. Find the fraction.​

Answer 1

Answer:

$\frac{3}{4\\}$

Step-by-step explanation:

let the numerator be x and denominator y

So, x+y=7

     y=7-x ------- eq 1

     4x=5y-8 -----eq2

     substituting eq 1 in eq 2 we get

      4x=35-5x-8

      9x=27

      x=3

and y =4

Answer 2

Let us take the numerator to be "x".

Let the denominator be "y".

∴ The fraction will be x/y.

According to the question;

• Numerator + Denominator = 7

• x + y = 7 → Equation(1)

Also according to the question;

• 4(Numerator) = 5(Denominator) - 8

• 4x = 5y - 8

• 4x - 5y = - 8 → Equation(2)

Multiplying Equation(1) by 5 we get;

⇔ 5(x + y) = 5(7)

⇔ 5x + 5y = 35 → Equation(3)

Adding Equation 2 & Equation 3 we get;

⇒ 5x + 5y + (4x - 5y) = 35 + (-8)

⇒ 5x + 5y + 4x - 5y = 35 - 8

⇒ 5x + 4x = 27

⇒ 9x = 27

⇒ x = 27/9

⇒ x = 3

Substitute the value of "x" in Equation(2).

⇒ 4x - 5y = - 8

⇒ 4(3) - 5y = - 8

⇒ 12 - 5y = - 8

⇒ 12 + 8 = 5y

⇒ 20 = 5y

⇒ y = 20/5

⇒ y = 4

We know that;

$\sf \Longrightarrow Fraction = \dfrac{x}{y}$

$\sf \Longrightarrow Fraction = \dfrac{3}{4}$

∴ Your answer will be 3/4.