Let x be the smaller income and y be the bigger income.
So, if both earn together $28,000, then:
[tex]x+y=28000[/tex]
If one earns $2000 more than the other, we can say the the bigger minus the smaller is equal to 2000, that is:
[tex]y-x=2000[/tex]
Now, we can solve the second equation for y and input it into the first equation:
[tex]\begin{gathered} y-x=2000 \\ y=x+2000 \end{gathered}[/tex][tex]\begin{gathered} x+y=28000 \\ x+x+2000=28000 \\ 2x=28000-2000 \\ 2x=26000 \\ x=\frac{26000}{2} \\ x=13000 \end{gathered}[/tex]
Thus, the smalle income is $13,000, alternative D.
