Question

Please answer guys:
a) If 6/2y - (3-4y) = 2/3 the. the value of y.
b) The denominator of a rational number is greater than its numerator by 5. If the numerator is increased by 12 and denominator is decreased by 3,the obtained rational number is 5/3. The rational number is :

Answer 1

Answer:-

a) 6/2y - (3 - 4y) = 2/3

→ 6/2y - 3 + 4y = 2/3

→ (6 - 6y + 8y)/2y = 2/3

→ (2y - 6)/2y = 2/3

After cross multiplication we get,

→ 6y - 18 = 4y

→ 6y - 4y = 18

→ 2y = 18

→ y = 18/2

→ y = 9

Hence, the value of y is 9.

b) Let the rational number be x/y.

Given:

Denominator = Numerator + 5

→ y = x + 5 -- equation (1)

And,

If the numerator is increased by 12 and denominator is decreased by 3 , the rational number obtained is 5/3.

→ (x + 12)/(y - 3) = 5/3

Substitute the value of "y" here.

→ (x + 12)/(x + 5 - 3) = 5/3

→ (x + 12)/(x + 2) = 5/3

→ 3x + 36 = 5x + 10

→ 3x - 5x = 10 - 36

→ - 2x = - 26

→ x = - 26/- 2

→ x = 13

Substitute the value of "x" in equation (1).

→ y = x + 5

→ y = 13 + 5

→ y = 18

Hence, the number x/y is 13/18.