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?
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.
Let's assume that the number of fish in Namira's tank is "x."
According to the given information, if Namira gives 6 fish to Lydia, Lydia will have 3 times as many fish as Namira. This can be expressed as:
(x + 6) = 3x
Subtracting "x" from both sides of the equation, we get:
6 = 2x
Dividing both sides of the equation by 2, we get:
x = 3
So, Namira has 3 fish in her tank.
If Namira gives 6 fish to Lydia, Lydia will receive 6 more fish, making her total number of fish (x + 6) = 3 + 6 = 9.
Thus, Lydia has 9 fish in her tank.
Therefore, Namira has 3 fish, and Lydia has 9 fish.