A scientist needs 80 liters of a 30% acid solution. He currently has a 20% solution and a 60% solution. How many liters of each does he need to make the needed 80 liters of 30% acid solution?

Question

A scientist needs 80 liters of a 30% acid solution. He currently has a 20% solution and a 60% solution. How many liters of each does he need to make the needed 80 liters of 30% acid solution?

Answer 1

To solve this problem, we can use a technique called the "mixture problem." Let's break it down step-by-step:

Step 1: Define variables
Let's call the amount of the 20% solution x (in liters) and the amount of the 60% solution y (in liters).

Step 2: Write equations
We need to set up two equations based on the given information:
- Equation 1: The total volume of the solution is 80 liters: x + y = 80
- Equation 2: The total amount of acid in the solution is 30% of 80 liters: (0.2x + 0.6y) = 0.3 * 80

Step 3: Solve the equations
To solve this system of equations, we'll use the substitution method. Rearrange equation 1 to solve for x: x = 80 - y. Substitute this value into equation 2:

0.2(80 - y) + 0.6y = 24
16 - 0.2y + 0.6y = 24
0.4y = 8
y = 20

Now, substitute the value of y into equation 1 to solve for x:

x + 20 = 80
x = 60

Thus, the scientist needs 60 liters of the 20% solution and 20 liters of the 60% solution to make the required 80 liters of the 30% acid solution.

Answer 2

To determine how many liters of each solution the scientist needs to make the 80 liters of 30% acid solution, we can set up a system of equations.

Let's assume the number of liters of the 20% solution required is 'x', and the number of liters of the 60% solution required is 'y'.

We can write the following equations based on the given information:

Equation 1: x + y = 80 (the total volume of the solution should be 80 liters)
Equation 2: 0.20x + 0.60y = 0.30(80) (the total amount of acid in the solution should be 30% of 80 liters)

Now, let's solve this system of equations:

From Equation 1, we can solve for 'x' in terms of 'y':
x = 80 - y

Substituting this value of x in Equation 2:
0.20(80 - y) + 0.60y = 0.30(80)
16 - 0.20y + 0.60y = 24
0.40y = 24 - 16
0.40y = 8
y = 8 / 0.40
y = 20

Substituting the value of y back into Equation 1:
x + 20 = 80
x = 80 - 20
x = 60

Therefore, the scientist needs 60 liters of the 20% solution and 20 liters of the 60% solution to make the required 80 liters of 30% acid solution.

Answer 3

If he uses x liters of 20%, then the rest (80-x) must be 60%. Now just look at the amounts of acid present:

.20x + .60(80-x) = .30*80

A scientist needs 80 liters of a 30​% acid solution. He currently has a 20% solution and a 60% solution. How many liters of each does he need to make the needed 80 liters of 30​% acid​ solution?

To solve this problem, we can use a technique called the "mixture problem." Let's break it down step-by-step:

To determine how many liters of each solution the scientist needs to make the 80 liters of 30% acid solution, we can set up a system of equations.

If he uses x liters of 20%, then the rest (80-x) must be 60%. Now just look at the amounts of acid present:

A scientist needs 80 liters of a 30% acid solution. He currently has a 20% solution and a 60% solution. How many liters of each does he need to make the needed 80 liters of 30% acid solution?