Question

Question #c35bd

Answer 1

Let `x/y` be the fraction.
Translating the words into equations:

`y=1+2x`

`(x+1)/(y+1)=1/2`

With these two equations with two variables, we can substitute the first equation into the second:
`(x+1)/(1+2x+1)=1/2`

`frac{cancel((x+1))}{2cancel((x+1))}=1/2`

`1/2=1/2`

This means that the set of equations will work for any value of x. For the sake of the answer key, let's choose `x=4`.
Check with the first equation ->`y=9, 5/10=1/2`
The answer key says the answer is 5/9, when it can't be 5/9.