Question

The sum of the numerator and the denominator of a fraction is equal to 12. Three times the numerator is 20 less than 5 times the denominator . Find the fraction 1) 4/8 2) 5/7 3) 3/4​

Answer 1

Answer:

2) 5/7

Step-by-step explanation:

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

Sum of the numerator and denominator of the fraction = 12

x + y = 12

x = 12 - y

Three times the numerator = 20 less than 5 times the denominator

3x = 5y - 20

Substituting x = 12 - y in the above equation

3( 12 - y) = 5y - 20

36 - 3y = 5y - 20

36 + 20 = 5y + 3y

56 = 8y

y = 56/8

y = 7

Substituting the value of y in x = 12 - y

x = 12 - 7

x = 5

Numerator = 5

Denominator = 7

Therefore the fraction is 5/7