Can't get to solve this word problem Price of lemon juice bottle is $4$ , price of orange juice bottle is $6$.
A buyer bought $20$ bottles and the total cost is $96$. 
How many lemon bottles and orange bottles did the buyer get? 
I know the answer but I don't know the steps to get to it.
 A: $a$ — number of lemon juice bottles,
$b$ — number of orange juice bottles.
Then $a+b=20$ because the buyer bought $20$ of them, and $4a+6b=96$ because cost of $a$ bottles (each costs $4$) plus $b$ bottles (each costs $6$) is equal to $96$. Finally, you have two equations
$$\begin{cases}
a+b=20\\
4a+6b=96
\end{cases}$$
Calculate $b$ from first equation ($b=20-a$) and plug it to the second equation
$$4a+6(20-a)=96$$
$$4a+120-6a=96$$
$$24=2a\implies a=12$$
Since $a+b=20$ we get $b=20-12=8$. The final answer is $$\begin{cases}a=12\\b=8\end{cases}$$
A: Let's call the number of lemon juice bottles bought $x$ and the number of OJ bottles bought $y$. Then the total number of bottles bought is:
$$ x + y =20$$
And the money payed for them:
$$4x+6y=20$$
Solving this system you get the number of bottles bought of each kind.
A: The way of getting this system is explained by others, I gonna help with solving that system!
$$
\begin{cases}
4x+6y=96 \\
x+y=20
\end{cases}\Longleftrightarrow
$$
$$
\begin{cases}
4x+6y=96 \\
y=20-x
\end{cases}\Longleftrightarrow
$$
$$
\begin{cases}
4x+6(20-x)=96 \\
y=20-x
\end{cases}\Longleftrightarrow
$$
$$
\begin{cases}
4x+120-6x=96 \\
y=20-x
\end{cases}\Longleftrightarrow
$$
$$
\begin{cases}
120-2x=96 \\
y=20-x
\end{cases}\Longleftrightarrow
$$
$$
\begin{cases}
-2x=96-120 \\
y=20-x
\end{cases}\Longleftrightarrow
$$
$$
\begin{cases}
2x=24 \\
y=20-x
\end{cases}\Longleftrightarrow
$$
$$
\begin{cases}
x=12 \\
y=20-x
\end{cases}\Longleftrightarrow
$$
$$
\begin{cases}
x=12 \\
y=20-12
\end{cases}\Longleftrightarrow
$$
$$
\begin{cases}
x=12 \\
y=8
\end{cases}
$$
