Answer:
Step-by-step explanation:
This is kinda tricky, but not nearly as bad as d = rt problems. Those are a nightmare!
We will make a table for this:
#lbs solution * % salt = lbs. salt
3% solution
- Water
New solution
And we will now fill in what we know. The 3% solution part is easy. The number of pounds of that is 50 and the percent salt in 3% salt is....well, 3%. As a decimal, it is .03:
#lbs solution * %salt = lbs salt
3% solution 50 * .03 = 1.5
- Water
New solution
The last column there with a 1.5 in it is the product of 50 times .03, since that is what the formula at the top of the table tells us we have to use. Now for the water. That's easy, too, since the amount of water we are evaporating (notice the subtraction sign out front of the word "water"; that indicates we are removing water) is our unknown, and we also know that water has 0% salt in it:
#lbs solution * %salt = lbs. salt
3% solution 50 * .03 = 1.5
- Water x * 0 = 0
New solution
Now all we have left is the new solution row and the equation. Finding the equation from a mixture table is as easy as it can be! Super easy!
The new solution will be 50 - x since, going down column 1, we are subtracting the water from the 3% solution, the % salt is to be 5%:
#lbs. solution * %salt = lbs. salt
3% solution 50 * .03 = 1.5
- Water x * 0 = 0
New solution 50 - x * .05 = 2.5 - .05x
Now we're ready for our equation. I got the 2.5 - .05x from multiplying
.05(50 - x), just so you know.
if we had to subtract the water from the salt solution and set it equal to the new solution in the first column, we also have to do it in the third column:
1.5 - 0 = 2.5 - .05x and solve for x:
-1 = -.05x so
x = 20 pounds of water
