A container holding 50 liters of a fruit juice blend has a juice concentration of 65%. How much pure fruit juice (in liters) should be mixed into this blend to elevate the juice concentration to 80%?

The correct option is 37.5 L.

Step 1: Determine the initial quantity of pure fruit juice
The container initially holds 50 liters of blend with a fruit juice concentration of 65% (or 0.65).
To find the volume of pure fruit juice in the mixture, multiply the total volume by the concentration fraction:

$\text{Initial Pure Juice}=50\times 0.65=32.5\text{liters}$

Step 2: Set up an equation for the new blend
Let $x$ represent the volume (in liters) of pure fruit juice added to the blend.
Adding $x$ liters of pure fruit juice increases both the total volume of pure juice and the total volume of the entire solution:
- New pure juice volume = $32.5+x$ liters
- New total blend volume = $50+x$ liters

We want the final concentration of fruit juice to be 80% (or 0.80). Setting the ratio of pure juice to total blend volume equal to 0.80 gives the equation:

$\frac{32.5+x}{50+x}=0.80$

Step 3: Solve the equation step-by-step
Multiply both sides of the equation by $(50+x)$:

$32.5+x=0.80\times (50+x)$

Distribute 0.80 on the right-hand side:

$32.5+x=40+0.80x$

Subtract $0.80x$ from both sides to gather terms containing $x$ on the left:

$x-0.80x=40-32.5$

Simplify both sides:

$0.20x=7.5$

Divide both sides by 0.20 to solve for $x$:

$x=\frac{7.5}{0.20}=37.5$

Conclusion
Therefore, 37.5 liters of pure fruit juice must be added to elevate the total juice concentration to 80%.