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.