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A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 40% salt and Solution B is 90%

salt. She wants to obtain 70 ounces of a mixture that is 80% salt. How many ounces of each solution should she use?
Solution A:
Solution B:
I Don't Know
ounces
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User Rjss
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1 Answer

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Answer:

The scientist should use 56 ounces of Solution B (Solution B: 56 ounces) and the remaining 14 ounces (Solution A: 14 ounces) to achieve a mixture that is 80% salt.

Explanation:

Step 1:

Let's denote the number of ounces of Solution A as "x" and the number of ounces of Solution B as "y".

To find the amounts of each solution needed, we can set up a system of equations based on the given information:

Step 2:

Equation 1: The total number of ounces in the mixture is 70: x + y = 70

Equation 2: The mixture is required to be 80% salt, so the amount of salt in Solution A and Solution B combined should be 80% of the total mixture: (0.40x + 0.90y) / 70 = 0.80

Now we can solve the system of equations to find the values of x and y.

Step 3:

From Equation 1, we can express x in terms of y: x = 70 - y

Substituting this value into Equation 2:

(0.40(70 - y) + 0.90y) / 70 = 0.80

Simplifying the equation:

(28 - 0.40y + 0.90y) / 70 = 0.80

(0.50y + 28) / 70 = 0.80

0.50y + 28 = 0.80 * 70

0.50y + 28 = 56

0.50y = 56 - 28

0.50y = 28

y = 28 / 0.50

y = 56

Final answer

Therefore, the scientist should use 56 ounces of Solution B (Solution B: 56 ounces) and the remaining 14 ounces (Solution A: 14 ounces) to achieve a mixture that is 80% salt.

User Nikaaner
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