desiguy wrote:
Solution A is 20% salt and Solution B is 80% salt. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% salt solution?
A. 6:4
B. 6:14
C. 4:4
D. 4:6
E. 3:7
We see that we need 25 ounces of salt. We can go through the choices:
A) 6:4
6x + 4x = 50
10x = 50
x = 5
So we have 6(5) = 30 ounces of A and 4(5) = 20 ounces of B. Does this produce 25 ounces of salt?
30 x 0.2 + 20 x 0.8 = 6 + 16 = 22 → No
B) 6:14
6x + 14x = 50
20x = 50
x = 2.5
So we have 6(2.5) = 15 ounces of A and 14(2.5) = 35 ounces of B. Does this produce 25 ounces of salt?
15 x 0.2 + 35 x 0.8 = 3 + 28 = 31 → No
C) 4:4
This means we have 25 ounces of A and 25 ounces of B. Does this produce 25 ounces of salt?
25 x 0.2 + 25 x 0.8 = 5 + 20 = 25 → Yes!
Alternate Solution:
Let A be the amount of Solution A and B be the amount of Solution B that produces a 50% salt solution when mixed. Since we want 50 ounces of 50% salt solution, there must be 50 x 0.5 = 25 ounces of salt in our solution.
We have the following:
A + B = 50
0.2A + 0.8B = 25
Let’s rewrite these two equations:
2A + 2B = 100
2A + 8B = 250
Let’s subtract the first equation from the second:
6B = 150
B = 25
Since A + B = 50, A = 25 also. Since there are A = 25 ounces of solution A and B = 25 ounces of solution B in our mixture, we need to mix A and B in the ratio of 1:1; or equivalently, 4:4.
Answer: C
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