Question

The sum of the numerator and 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

Let the numerator be x and the denominator be y
The fraction = x/y
A/Q
X + Y = 7 - - - - - - - - - - - equation 1
Again case II
4X = 5Y - 8
4 X - 5Y = - 8 - - - - - - - - - - EQUATION 2

USING Elimination method
Multiplying eqn 1 with 4 we get

4x+4y = 28
4x-5y = - 8
- + +
We get
9y = 36
Y= 4
Now putting the value of y in eqn 1 we get
X+4 =7
X = 3
Therefore the numerator is 3 and the denominator is 7

So the fraction is 3/7

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Answer 2

Answer:

$\large{\underline{\boxed{\sf \dfrac{3}{4}}}}$

Step-by-step explanation:

Let the numerator of the fraction be x and the denominator be y.

∴ Original fraction = $\dfrac{x}{y}$

Given that :

Sum of numerator and denominator is 7.

⇒ x + y = 7 .....(i)

Also,

Four times numerator is 8 less than 5 times the denominator.

⇒ 4x = 5y - 8

⇒ 4x - 5y = - 8 ....(ii)

Here, we got two equations. In order to get solution, multiply equation (i) by 4.

4(x + y) = 4 * 7

⇒ 4x + 4y = 28 ... (iii)

Subtracting eqⁿ (ii) from (iii) -

4x + 4y - (4x - 5y) = 28 - (-8)

⇒ 4x + 4y - 4x + 5y = 28 + 8

⇒ 9y = 36

⇒ y = $\dfrac{36}{9}$

⇒ y = 4

Substituting the value of y in (i) -

⇒ x + y = 7

⇒ x + 4 = 7

⇒ x = 7 - 4

⇒ x = 3

Hence, the required fraction is $\bf \dfrac{3}{4}.$