@ai which is the right answer

Question

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)

Answer 1

To determine the amount of the 5% solution (let's call it \(x\) liters) and the amount of the 40% solution (which will be \(10 - x\) liters, since the total volume must be 10 liters), we can set up an equation based on the total amount of acid in the final mixture.

The target is to create 10 liters of a 20% solution, which means the total amount of acid needed is: \[ 0.20 \times 10 = 2 \text{ liters of acid} \]

The amount of acid contributed by the 5% solution is: \[ 0.05x \text{ liters of acid} \]

The amount of acid contributed by the 40% solution is: \[ 0.40(10 - x) \text{ liters of acid} \]

To find the correct equation, we set the total amount of acid equal to the amount needed (2 liters): \[ 0.05x + 0.40(10 - x) = 2 \]

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

Thus, the correct answer is B.

Answer 2

@ ai answer this using the previos equation

Answer 3

Sure! Let's use the equation from option B to solve for \(x\). The equation is:

\[ (0.20)(10) = 0.05x + 0.40(10 - x) \]

First, calculate the left-hand side:

\[ (0.20)(10) = 2 \]

Now we rewrite the equation:

\[ 2 = 0.05x + 0.40(10 - x) \]

Next, distribute \(0.40\) on the right-hand side:

\[ 2 = 0.05x + 4 - 0.40x \]

Combine the \(x\) terms:

\[ 2 = 4 - 0.35x \]

Now, isolate the term with \(x\):

\[ 0.35x = 4 - 2 \] \[ 0.35x = 2 \]

Now, solve for \(x\):

\[ x = \frac{2}{0.35} \approx 5.71 \text{ liters (of the 5% solution)} \]

To find the amount of the 40% solution, use:

\[ 10 - x = 10 - 5.71 \approx 4.29 \text{ liters (of the 40% solution)} \]

Summary of the solution:

• 5% solution: approximately 5.71 liters
• 40% solution: approximately 4.29 liters

This means the scientist should mix approximately 5.71 liters of the 5% solution and 4.29 liters of the 40% solution to obtain 10 liters of a 20% acid solution.