Question

The sum of the numerator and denominator of a fraction expressed in simplest form is 17. If 3 is added to the numerator, the value of the fraction will be 1. What is the fraction?

Answer 1

X is represented as the numerator, y is the denominator.
x+y=17

x+3/y =1

If x+3/y is 1, x+3 must equal y. Use the first equation to solve for y.
y=17-x
Plug in the first equation.
x+3 = y
x+3= 17-x
x+3+x=17-x+x (Add x)
2x+3=17
2x+3-3=17-3 (subtract 3)
2x=14
x=7.
Plug in x into original equation (x+y=17)
7+y=17
y=10

The fraction is 7/10.

Answer 2

x+y=17 solve for a variable and plug into the 2nd equation
(x+3)/y=1 also could be written as x+3=y
x=17-y
17-y+3=y combine and add y over to other side
20=2y
y=10
plug back in x+10=17
x=7
so the original fraction is 7/10