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Tasha needs 75 liters of a 40% solution of alcohol. She has a 20% solution and a 50% solution available. How many liters of the 20% solution and how many liters of the 50% solution should she mix to make the 40% solution?

Respuesta :

frika

Answer:

Tasha should mix 25 liters of 20% solution and 50 liters of 50%.

Step-by-step explanation:

Let x liters be the amount of 20% solution  and y liters be the amount of 50% solution Tasha takes.

1. Tasha needs 75 liters of a 40% solution of alcohol. Then

x + y = 75

2. There are

  • [tex]0.2x[/tex] liters of alcohol in x l of 20% solution
  • [tex]0.5y[/tex] liters of alcohol in 50% solution
  • [tex]0.4\cdot 75=30[/tex] liters of alcohol in 75 liters of 40% solution

In total, [tex]0.2x+0.5y[/tex] of alcohol that is 30 l, so

0.2x + 0.5y = 30

3. Solve the system of two equations:

[tex]\left\{\begin{array}{l}x+y=75\\ \\0.2x+0.5y=30\end{array}\right.[/tex]

From the first equation:

[tex]x=75-y[/tex]

Substitute it into the second equation

[tex]0.2(75-y)+0.5y=30\\ \\15-0.2y+0.5y=30\\ \\0.3y=30-15\\ \\0.3y=15\\ \\3y=150\\ \\y=50\\ \\x=75-50=25[/tex]

Tasha should mix 25 liters of 20% solution and 50 liters of 50%.

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