the manager at a health foods store is mixing a 75 - liter batch of his superfruit juice cocktail. the…

the manager at a health foods store is mixing a 75 - liter batch of his superfruit juice cocktail. the cocktail, which costs $34.05 per liter to make, combines mixed fruit juice costing $4.30 per liter and acai berry juice costing $46.80 per liter. how many liters of each should he mix together to make the cocktail? write your answers as whole numbers or as decimals rounded to the nearest tenth. liters of mixed fruit juice liters of acai berry juice

the manager at a health foods store is mixing a 75 - liter batch of his superfruit juice cocktail. the cocktail, which costs $34.05 per liter to make, combines mixed fruit juice costing $4.30 per liter and acai berry juice costing $46.80 per liter. how many liters of each should he mix together to make the cocktail? write your answers as whole numbers or as decimals rounded to the nearest tenth. liters of mixed fruit juice liters of acai berry juice

Answer

Explanation:

Step1: Set up equations

Let $x$ be the volume of mixed - fruit juice and $y$ be the volume of acai - berry juice. We have two equations:

  1. $x + y=75$ (total volume equation), so $y = 75 - x$.
  2. The cost - based equation: $4.3x+46.8y=34.05\times75$.

Step2: Substitute $y$ into the cost equation

Substitute $y = 75 - x$ into $4.3x + 46.8y=34.05\times75$. $4.3x+46.8(75 - x)=34.05\times75$. Expand: $4.3x+3510-46.8x = 2553.75$. Combine like terms: $4.3x-46.8x=2553.75 - 3510$. $-42.5x=2553.75 - 3510=-956.25$.

Step3: Solve for $x$

$x=\frac{-956.25}{-42.5}=22.5$.

Step4: Solve for $y$

Since $y = 75 - x$, then $y=75 - 22.5 = 52.5$.

Answer:

22.5 liters of mixed fruit juice 52.5 liters of acai berry juice