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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

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