Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

How many 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

How Many 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 class=

Sagot :

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