Question

A numerator of a fraction is 7 less than it's denominator. If 4 is subtracted from the numerator and the denominator is increased by 1, the resulting fraction equals 1/3. Find the fraction.

Answer 1

Answer:

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

according to the question-

x=y-7

or x-y=-7(eq 1)

x-4/y+1=1/3 or 3x-y=13 (eq 2)

from eq 1 and 2 we get

x-y=-7

3x-y=13

-2x=-20

x=10

putting x value in eq 1 we get

10-y=-7

y=17

so 10/17 is the required fraction.

Step-by-step explanation:

Answer 2

Answer:

let the numberator be y and the denominator be x

y=x-7

y-x=-7. (equation no .1)

y-4/x+1=1/3

by cross multiplying

3y-12=x+1

3y-x=1+12

3y-x= 13. ( equation no.2)

from equation 1 and2

y-x-3y +x= 13+7

cut -x by +x and subtracting y from 3y

-2y=20

y=20/-2

y=-10

from equation no 1

-10-y=-7

-y=-7-10

-y=-17

minus - minus cancel

the fraction is 10/17