Answer :
[tex]At\ the\ beginning\ :\\3x-\ number\ of\ bottles\ of\ apple\ juice\\\\
2x-\ number\ of\ bottles\ of\ orange juice\\\\
After\ sale:\\
1x-number\ of\ bottles\ of\ apple\ juice\\\\
6x- number\ of\ bottles\ of\ orange juice\\\\
\frac{3x-64}{2x}=\frac{1x}{6x}\\\\
\frac{3x-64}{2x}=\frac{1}{6}\\\\Cross\ multiplication:\\\\
6(3x-64)=2x\\
18x-384=2x\ \ \ |subtract\ 2x\\
16x-384=0\ \ \ |add\ 384\\
16x=384\ \ | divide\ by\ 16\\\\x=24
He\ had\ 24\ bottles\ of\ apple\ juice\ and\ 144 \ of\ orange\ juice.[/tex]
If the ratio of the number of bottles of apple juice to the number of bottles of orange juice was 3:2, then you can denote 3x - the number of bottles of apple juice and 2x - the number of bottles of orange juice.
After he sold 64 bottles of apple juice, the number of bottles of apple juice became 3x-64 and the number of bottles of orange juice remained 2x.
The new ratio is 1:6, this means that
[tex]\dfrac{3x-64}{2x}=\dfrac{1}{6}.[/tex]
Solve this equation:
[tex](3x-64)\cdot 6=2x\cdot 1,\\18x-384=2x,\\18x-2x=384,\\16x=384,\\ \\x=\dfrac{384}{16}=24.[/tex]
In the end Mr. Young had:
- [tex]3x-64=3\cdot 24-64=8[/tex] bottles of apple juce;
- [tex]2x=2\cdot 24=48[/tex] bottles of orange juice.