How many kilograms of water must be evaporated from 10kg of an 8% salt solution to produce a 25% salt solution
let the amount evaporated be x kg
so shouldn't
.25(10-x) = .08(10)
(I got x = 6.8 kg)
Why did the salt go to school? Because it wanted to be a high percentage solution!
To solve this problem, let's set up a little salt comedy act.
We have 10kg of an 8% salt solution. That means we have 0.8kg (10kg * 8%) of salt in total.
Now, we want to evaporate some water to make a 25% salt solution. Let's say we evaporated 'x' kilograms of water.
After evaporating 'x' kilograms of water, we are left with (10kg - x) kilograms of solution. Since we're aiming for a 25% salt concentration, we want the amount of salt to be 25% of the total solution.
So, (0.25 * (10kg - x)) should equal the amount of salt, which is 0.8kg.
Now, let's solve this salt-themed equation and you'll have your answer in no time!
To solve this problem, we need to calculate the amount of water that needs to be evaporated from the 10kg of an 8% salt solution to obtain a 25% salt solution.
Step 1: Find the initial amount of salt in the solution.
Initial amount of salt = 8% of 10kg
= (8/100) × 10kg
= 0.8kg
Step 2: Find the final amount of salt needed in the solution.
Final amount of salt = 25% of (10kg - x)
= (25/100) × (10kg - x)
= 2.5kg - 0.025x kg (where x is the mass of water evaporated in kg)
Step 3: Equate the initial and final amounts of salt.
0.8kg = 2.5kg - 0.025x
Step 4: Rearrange the equation to solve for x.
0.025x = 2.5kg - 0.8kg
0.025x = 1.7kg
x = 1.7kg / 0.025
x ≈ 68kg
Therefore, approximately 68 kilograms of water must be evaporated from the 10kg of an 8% salt solution to produce a 25% salt solution.
To find out how many kilograms of water must be evaporated from a 10kg 8% salt solution to produce a 25% salt solution, we can follow these steps:
Step 1: Calculate the amount of salt in the initial solution:
Multiply the mass of the initial solution (10kg) by the percentage of salt (8% = 0.08).
Salt content = 10kg * 0.08 = 0.8 kg
Step 2: Set up an equation:
The amount of salt in the final solution will be the same as in the initial solution. Let's assume that x kilograms of water evaporate. Thus, the salt content will be 0.8 kg.
0.8 kg = x kg * 0.25
Step 3: Solve the equation:
0.8 kg = 0.25x
Divide both sides by 0.25 to isolate x:
x = 0.8 kg / 0.25 = 3.2 kg
So, 3.2 kilograms of water must be evaporated from the 10kg of an 8% salt solution to produce a 25% salt solution.