Question 897081
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.