Respuesta :
Let x and y represent the amount of the first and second type of fruit drinks (respectively) that are used to create the fruit drink that contains 85% fruit juice.
The total volume of the mixture is x+y and it must be equal to 160:
[tex]x+y=160[/tex]Since the first mixture contains 20% fruit juice, only 0.2x of the volume x is pure fuit juice. The total amount of fruit juice in the mixture will be 0.2x plus y, and must be equal to 85% of 160:
[tex]0.2x+y=0.85\cdot160[/tex]We got a system with two variables and two equations. Solve the system of equations using the elimination method:
[tex]\begin{gathered} x+y=160 \\ 0.2x+y=0.85\cdot160 \\ \Rightarrow x-0.2x+y-y=160-0.85\cdot160 \\ \Rightarrow0.8x=160-136 \\ \Rightarrow0.8x=24 \\ \Rightarrow x=\frac{24}{0.8} \\ \therefore x=30 \end{gathered}[/tex]Replace x=30 into the first equation to find the value of y:
[tex]\begin{gathered} x+y=160 \\ \Rightarrow30+y=160 \\ \Rightarrow y=160-130 \\ \Rightarrow y=130 \end{gathered}[/tex]Then, 30 pints of the 20% pure fruit juice and 130 pints of the 100% pure fruit juice are needed to produce 160 pints of the 85% pure fruit juice mixture.
Therefore, the answer is:
[tex]\begin{gathered} \text{First fruit drink = 30 pints} \\ \text{Second fruit drink = 130 pints} \end{gathered}[/tex]