A tank had 20 clownfish and angelfish. 4 clownfish were sold and some angelfish were added to the tank such that the number of angelfish increased by 50%. After that, there were 18 fish in the tank altogether. How many clownfish were there in the tank at first?
How do I create an algebraic expression for this?
On
In the beginning, there are a total of $20$ fish in the tank. Let's mark $C$= number of clownfish in the beginning and $A=$number of angelfish in the beginning. Now we know that $$ C+A = 20 $$ Then 4 clownfish were sold, resulting in $C$ getting replaced by $C-4$. Then the number of angelfish is increased by $50~\%$, meaning that $A$ is replaced by $\frac{3}{2}A$. So at the end we have 18 fish $$ (C-4) + \frac{3}{2}A = 18 $$ Simplifying the equations, we get the following pair of equations: $$ \left\{ \begin{array}{cccc} C &+ A &=& 20 \\ 2C &+ 3A &=& 44 \end{array} \right. $$ Do you know how to solve this now?
You have $c+a=20$.
The clownfish were sold, so c becomes $c-4$.
The angelfish population increases by $50\%$, so $a$ become $1.50a$.
Now, we have $c-4+1.50a=18$.