Explanation:
Let x be the number of ounces of 20% saline solution needed, and y be the number of ounces of 70% saline solution needed to obtain 25 ounces of a 50% saline solution.
To solve the problem, we can use the fact that the amount of salt in the final mixture must equal the sum of the amounts of salt in the two original solutions. That is:
0.2x + 0.7y = 0.5(25)
Simplifying this equation gives:
0.2x + 0.7y = 12.5
We also know that the total amount of solution is 25 ounces, so:
x + y = 25
We now have two equations with two variables, which we can solve using algebra. Rearranging the second equation to solve for x in terms of y, we get:
x = 25 - y
Substituting this expression for x into the first equation, we get:
0.2(25 - y) + 0.7y = 12.5
Multiplying out the terms and simplifying gives:
5 - 0.2y + 0.7y = 12.5
0.5y = 7.5
y = 15
Substituting this value for y into the equation x = 25 - y, we get:
x = 25 - 15 = 10
Therefore, we need 10 ounces of the 20% saline solution and 15 ounces of the 70% saline solution to obtain 25 ounces of a 50% saline solution.