Given:
The first type is 20% pure fruit juice, and the second type is 70% pure fruit juice.
To find:
The amount in pints of each of the existing types of drink must be used to make 70 pints of a mixture that is 35% pure fruit juice.
Explanation:
Let x be the number of pints in the first type.
Let y be the number of pints in the second type.
According to the problem,
[tex]\begin{gathered} x+y=70...............(1) \\ 20\%\text{ of }x+70\%\text{ of }y\text{ }=35\%\text{ of }70 \\ 0.2x+0.7y=24.5........(2) \end{gathered}[/tex]Multiply equation (1) by 0.2, and we get
[tex]0.2x+0.2y=14........(3)[/tex]Subtract (3) from (2), we get,
[tex]\begin{gathered} 0.5y=10.5 \\ y=\frac{10.5}{0.5} \\ y=21 \end{gathered}[/tex]Substituting into equation (1) we get,
[tex]\begin{gathered} x+21=70 \\ x=49 \end{gathered}[/tex]Final answer:
• First fruit drink: 49 pints
,• Second fruit drink: 21 pints