Answer:
Explanation:
Let x be the amount of 50% saline solution needed, and y be the amount of 10% saline solution needed.
To make 11 liters of a 30% saline solution, we know that:
The total amount of solution is 11 liters, so x + y = 11.
The total amount of salt in the solution is 30% of 11 liters, or 0.3 x 11 = 3.3 liters of salt.
The amount of salt contributed by the 50% saline solution is 0.5x liters of salt.
The amount of salt contributed by the 10% saline solution is 0.1y liters of salt.
Therefore, we can set up a system of two equations:
x + y = 11 (equation 1)
0.5x + 0.1y = 3.3 (equation 2)
To solve for x and y, we can use any method of solving systems of equations. Here, we'll use substitution:
From equation 1, we know that y = 11 - x. Substituting this into equation 2, we get:
0.5x + 0.1(11 - x) = 3.3
0.5x + 1.1 - 0.1x = 3.3
0.4x = 2.2
x = 5.5
So Joy needs 5.5 liters of the 50% saline solution. Substituting this into equation 1, we get:
5.5 + y = 11
y = 5.5
So Joy needs 5.5 liters of the 10% saline solution.
Therefore, to make 11 liters of a 30% saline solution, Joy needs to mix 5.5 liters of 50% saline solution and 5.5 liters of 10% saline solution.