Lydia and Namira both have some fish in their fish tanks. If Namira gives 6 fish to Lydia, Lydia will have 3 times as many fish as Namira. How many fish does each girl have?

Answer 1

Let's say Lydia has L fish and Namira has N fish.
If Namira gives 6 fish to Lydia, Lydia will have L+6 fish.
We know that L+6=3(N-6)
L+6=3N-18
L=3N-18-6
L=3N-24...........(1)
Using equation 1, we know that L= 3N-24
Also, if Namira gives 6 fish to Lydia, Lydia will have 3 times as many fish as Namira.
So L=3N-6..........(2)
We can set equation 1 and equation 2 equal to each other and isolate L and N.
3N-24=3N-6
3N-3N=-6+24
0=18
Since zero cannot be equal to 18, there is no solution to the equation.
Therefore, Lydia and Namira can't have the given number of fish, and the problem has no solution.