A barista blends 12 liters of concentrated syrup with x liters of milk to prepare a drink. If the syrup makes up 20% of the overall mixture volume, calculate the value of x.

The correct option is 48 liters.

Step-by-Step Explanation:

We are given that a barista blends 12 liters of concentrated syrup with x liters of milk to prepare a drink.

The volume of syrup is 12 liters, and the volume of milk is x liters.
Therefore, the total volume of the overall mixture is:

$\text{Total Volume}=12+x$

We are given that syrup makes up 20% of the overall mixture volume.
Expressing 20% as a decimal gives 0.20. We can write the proportion as:

$\frac{\text{Volume of Syrup}}{\text{Total Volume}}=0.20$

Substitute the known expressions into this equation:

$\frac{12}{12+x}=0.20$

To solve for x, multiply both sides of the equation by (12 + x):

$12=0.20\times (12+x)$

Distribute 0.20 across the terms inside the parentheses:

$12=2.4+0.20x$

Subtract 2.4 from both sides of the equation:

$12-2.4=0.20x$

$9.6=0.20x$

Divide both sides by 0.20 to isolate x:

$x=\frac{9.6}{0.20}$

$x=48$

Therefore, the value of x is 48 liters.