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Question
A scientist needs 60 liters of a 40% solution of alcohol. He has a 30% solution and a 60% solution available.
How many liters of the 30% solution and how many liters of the 60% solution should he mix to make the 40% solution?
Provide your answer below:
30% solution: liters, 60% solution:
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mathstudent55

Answer:

40 liters of the 30% solution and 20 liters of the 60% solution.

Step-by-step explanation:

These problems are solved by writing 2 equations. One equation deals with the total amounts of solutions. The other equation deals with the amounts of the named ingredient in the solutions which in this case is alcohol. Then you solve the 2 equations as a system of equations.

Let x = number of liters of the 30% alcohol solution.

Let y = number of liters of the 60% alcohol solution.

The scientist is making 60 liters of 40% solution.

The amounts of solutions he will use are:

x + y = 60     Eq. 1

The amount of alcohol in the 30% solution is 30% of x, which is 0.3x.

The amount of alcohol in the 60% solution is 60% of y which is 0.6y.

The amount of alcohol in the 60 liters of 40% solution is

40% of 60 liters = 0.4 × 60 = 24

0.3x + 0.6y = 24    Eq. 2

Equations 1 and 2 form a system of equations. We now solve them simultaneously.

x + y = 60

0.3x + 0.6y = 24

Let's use the substitution method.

Solve the first equation for x.

x = 60 - y

Substitute 60 - y for x in the second equation.

0.3x + 0.6y = 24

0.3(60 - y) + 0.6y = 24

18 - 0.3y + 0.6y = 24

0.3y = 6

y = 20

Now we substitute 20 for y in the first equation and solve for x.

x + y = 60

x + 20 = 60

x = 40

Answer: 40 liters of the 30% solution and 20 liters of the 60% solution.

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