SOLUTION: A solution that is 30% salt is mixed with a solution that is 40% salt. Which of the following ( 30%, 35%,39%, 40%, and 45%) are not possible choices for the concentration of salt i

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Question 897081: A solution that is 30% salt is mixed with a solution that is 40% salt. Which of the following ( 30%, 35%,39%, 40%, and 45%) are not possible choices for the concentration of salt in the resulting mixture.
Found 2 solutions by Theo, Alan3354:
Answer by Theo(13342) (Show Source):
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the mixture cannot be greater than or equal to 40% since any amount of the 30% salt solution will result in a mixture that is less than 40% salt.

for example:

assume you mixed 10 pounds of 30% solution with 100 pounds of 40% solution.

the amount of salt in the 30% solution is 3 pounds.
the amount of salt in the 40% solution is 40 pounds.

the amount of salt in the combined mixture is 43 pounds out of a total of 110 pounds which results in a ratio of 43/110 which is equal to 39.090909... percent.

it is mathematically impossible to get an overall mixture greater than or equal to 40 percent.

example:

.3 * x + .4 * 100 = .5 * (x + 100)

we want to find the value of x that will result in an overall mixture of 50%.

simplify the equation to get:

.3 * x + 40 = .5 * x + 50

subtract .5 * x from both sides of the equation and subtract 40 from both sides of the equation to get:

.3 * x - .5 * x = 50 - 40

simplify to get:

-.2 * x = 10

solve for x to get x = -50

the number of pounds of the 30% mixture can't be negative, so getting a 50% solution when you mix a 30% and a 40% solution together is impossible.

Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
45% is not possible.
Add a lesser concentration (30%) to 40% will not increase the concentration of the mix.
30% and 40% are possible if none of the other mix is used.
Equal amounts gives the average, 35%