Can't get to solve this word problem

Question

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.

Answer 1

The way of getting this system is explained by others, I gonna help with solving that system!

$$ \begin{cases} 4x+6y=96 \\ x+y=20 \end{cases}\Longleftrightarrow $$ $$ \begin{cases} 4x+6y=96 \\ y=20-x \end{cases}\Longleftrightarrow $$ $$ \begin{cases} 4x+6(20-x)=96 \\ y=20-x \end{cases}\Longleftrightarrow $$ $$ \begin{cases} 4x+120-6x=96 \\ y=20-x \end{cases}\Longleftrightarrow $$ $$ \begin{cases} 120-2x=96 \\ y=20-x \end{cases}\Longleftrightarrow $$ $$ \begin{cases} -2x=96-120 \\ y=20-x \end{cases}\Longleftrightarrow $$ $$ \begin{cases} 2x=24 \\ y=20-x \end{cases}\Longleftrightarrow $$ $$ \begin{cases} x=12 \\ y=20-x \end{cases}\Longleftrightarrow $$ $$ \begin{cases} x=12 \\ y=20-12 \end{cases}\Longleftrightarrow $$ $$ \begin{cases} x=12 \\ y=8 \end{cases} $$

Answer 2

$a$ — 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 $$\begin{cases}a=12\\b=8\end{cases}$$

Answer 3

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.