How much water must be evaporated from 16 ounces of 3% salt solution to make 4% salt solution?
let the amount of water to be evaporated be x ounces
0.03(16) = 0.04(16-x)
times 100
3(16) = 4(16-x)
48 = 64 - 4x
4x = 16
x = 4
To solve this problem, we need to calculate the amount of water that needs to be evaporated from the 3% salt solution to achieve a 4% salt solution.
Step 1: Determine the current amount of salt in the solution.
In a 16-ounce solution, 3% salt means there are 0.03 * 16 = 0.48 ounces of salt in the solution.
Step 2: Determine the desired amount of salt in the final solution.
To have a 4% salt solution, we need 4% of the total volume to be salt. Since the final volume will remain the same (16 ounces), the desired amount of salt is 0.04 * 16 = 0.64 ounces.
Step 3: Calculate the amount of water that needs to be evaporated.
The initial volume of water in the solution is 16 ounces minus the initial amount of salt, which is 16 - 0.48 = 15.52 ounces.
Let's assume we need to evaporate x ounces of water.
After evaporating x ounces of water, the final volume of water in the solution will be 15.52 - x ounces.
Step 4: Calculate the amount of salt after evaporating the water.
The final volume of the solution remains the same at 16 ounces, and the amount of salt is 0.64 ounces.
Thus, the final concentration of salt will be 0.64 / 16 = 0.04 or 4%.
So, the final amount of water in the solution is 15.52 - x ounces, and the final amount of salt is 0.64 ounces.
By setting up an equation, we can solve for x:
(0.64) / (16) = (0.04) / (15.52 - x)
Simplifying the equation:
0.04 * (15.52 - x) = 0.64 * 16
Further simplification:
0.6208 - 0.04x = 10.24
Rearranging the equation:
-0.04x = 9.6192
Solving for x by dividing both sides by -0.04:
x = 9.6192 / -0.04
Calculating x:
x ≈ -240.48
Since it is not possible to have negative volume of water, we can conclude that no water needs to be evaporated from the solution to achieve a 4% salt solution.
To find out how much water must be evaporated from a 16-ounce 3% salt solution to make a 4% salt solution, we need to calculate the initial amount of salt in the 16-ounce solution and the final amount of salt in the 4% solution.
First, let's find the initial amount of salt in the 16-ounce 3% salt solution:
Initial amount of salt = 3% of 16 ounces
= (3/100) x 16
= 0.03 x 16
= 0.48 ounces of salt
Now, let's calculate the final amount of salt in the 4% salt solution:
Final amount of salt = 4% of (16 - x) ounces (where x is the amount of water evaporated)
= (4/100) x (16 - x)
= 0.04 x (16 - x)
= 0.64 - 0.04x ounces of salt
To make the 16-ounce 3% salt solution into a 4% salt solution, the final amount of salt must be equal to the initial amount of salt:
0.64 - 0.04x = 0.48
Now, let's solve this equation:
0.64 - 0.04x - 0.48 = 0
0.16 - 0.04x = 0
-0.04x = -0.16
x = (-0.16)/(-0.04)
x = 4
Hence, 4 ounces of water must be evaporated from the 16-ounce 3% salt solution to make a 4% salt solution.