Question

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?

Answer 1

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

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

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

In total,
`0.2x+0.5y` of alcohol that is 30 l, so

0.2x + 0.5y = 30

3. Solve the system of two equations:

`\left\{\begin{array}{l}x+y=75\\ \\0.2x+0.5y=30\end{array}\right.`

From the first equation:

`x=75-y`

Substitute it into the second equation

`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`

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