Question

Mr.Young had some bottles of apple juice and orange juice. The ratio of the number of bottles of apple juice to the number of bottles of orange juice was 3:2. After he sold 64 bottles of apple juice, the ratio became 1:6. How many bottles of apple juice and orange juice did Mr.Young have altogether in the end

Answer 1

$At\ the\ beginning\ :\\3x-\ number\ of\ bottles\ of\ apple\ juice\\\\ 2x-\ number\ of\ bottles\ of\ orange juice\\\\ After\ sale:\\ 1x-number\ of\ bottles\ of\ apple\ juice\\\\ 6x- number\ of\ bottles\ of\ orange juice\\\\ \frac{3x-64}{2x}=\frac{1x}{6x}\\\\ \frac{3x-64}{2x}=\frac{1}{6}\\\\Cross\ multiplication:\\\\ 6(3x-64)=2x\\ 18x-384=2x\ \ \ |subtract\ 2x\\ 16x-384=0\ \ \ |add\ 384\\ 16x=384\ \ | divide\ by\ 16\\\\x=24 He\ had\ 24\ bottles\ of\ apple\ juice\ and\ 144 \ of\ orange\ juice.$

Answer 2

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

$\dfrac{3x-64}{2x}=\dfrac{1}{6}.$

Solve this equation:

$(3x-64)\cdot 6=2x\cdot 1,\\18x-384=2x,\\18x-2x=384,\\16x=384,\\ \\x=\dfrac{384}{16}=24.$

In the end Mr. Young had:

• $3x-64=3\cdot 24-64=8$ bottles of apple juce;
• $2x=2\cdot 24=48$ bottles of orange juice.