Question

@ai solve this


A scientist needs 10 liters of a 20% acid solution for an experiment, but she has only a 5% solution and a 40% solution. About how many liters of the 5% and the 40% solutions should the scientist mix to get the solution she needs?

Choose the equation to match the situation.
A. (0.20)(10) = 0.05x + 0.40x
B. (0.20)(10) = 0.05x + 0.40(10 − x)
C. (0.20)(10) = 0.05(10) + 0.40(10 − x)
D. (0.20)(10) = 0.05(10 − x) + 0.40(10 − x)
Part B

Round the answers to the nearest tenth.

She should mix
liters of 5% solution with
liters of 40% solution.

Answer 1

To determine how many liters of the 5% and 40% solutions the scientist should mix to obtain 10 liters of a 20% acid solution, we can formulate an equation based on the concentration of acid in each solution.

Let's denote:
- \( x \) = liters of the 5% solution
- \( 10 - x \) = liters of the 40% solution (since the total volume needs to be 10 liters)

We know:
- The desired concentration of acid in the final solution is 20%, which means there will be \( 0.20 \times 10 = 2 \) liters of acid in the final solution.

From the two solutions, we can express the total acid in the mixture:
- The 5% solution contributes \( 0.05x \) liters of acid.
- The 40% solution contributes \( 0.40(10 - x) \) liters of acid.

Thus, we can write the equation:
\[
0.20 \times 10 = 0.05x + 0.40(10 - x)
\]

This corresponds to option **B**:
\[
(0.20)(10) = 0.05x + 0.40(10 - x)
\]

### Part B: Solving the Equation
Now let's solve for \( x \):

1. Substitute \( 2 \) into the equation:
\[
2 = 0.05x + 0.40(10 - x)
\]

2. Distribute:
\[
2 = 0.05x + 4 - 0.40x
\]

3. Combine like terms:
\[
2 = 4 - 0.35x
\]

4. Rearrange to solve for \( x \):
\[
0.35x = 4 - 2
\]
\[
0.35x = 2
\]
\[
x = \frac{2}{0.35}
\]
\[
x \approx 5.7143 \ (\text{liters of 5% solution})
\]

5. Now find the amount of the 40% solution:
\[
10 - x = 10 - 5.7143 \approx 4.2857 \ (\text{liters of 40% solution})
\]

### Final Answer (Rounded):
- Liters of 5% solution: \( \approx 5.7 \)
- Liters of 40% solution: \( \approx 4.3 \)

The scientist should mix **5.7 liters of 5% solution** with **4.3 liters of 40% solution**.