Question

A bottle is 80% full. The liquid in the bottle consists of 60% guava juice and 40% pineapple juice. The remainder of the bottle is then filled with 200 mL of rum. How much guava juice is in the bottle ?

• A. $350$ mL
• B. $480$ mL
• C. $500$ mL
• D. $460$ mL

Answer 1

The correct option is B $480$ mL

You can begin by figuring out what the total amount of liquid is.If the bottle was 80% full, and adding 200 mL of rum made the bottle full, then 200 mL is equal to 20% of the total capacity of the bottle. Let b be the total capacity of the bottle:

$200=\frac{20}{100}b$

$200=\frac{1}{5}b$

$1000=b$

The bottle has a total capacity of 1,000 mL.

Now you can use a successive percent to figure out the total amount of guava juice. You know 80% of the bottle is filled with juice, and 60% of the juice is guava juice. In other words, guava juice is 60% of 80% of 1,000 mL:

$g=\left(\frac{60}{100}\right)\left(\frac{80}{100}\right)1000$

$g=\left(\frac{3}{5}\right)\left(\frac{4}{5}\right)1000$

$g=\left(\frac{3}{1}\right)\left(\frac{4}{1}\right)40$

$g=3\times 160$

$g=480$

There is 480 mL of guava juice.

Note that the last calculation, $3\times 4\times 40$, can be done in any order that is easiest for you. Most of the time, multiplying the largest numbers together first is easier in the long run