Thank you in advance for your kind help!
How much fresh water should be mixed to a 30% salt water solution, to obtain 90 gallons of a 23% salt water solution?
you want to decrease the concentration by 23/30, so that means you have to increase the volume by 30/23.
30/23 x = 90
x = 90 * 23/30 = 69
So, add 21 gallons of water
To solve this problem, we need to calculate the amount of fresh water that needs to be mixed with the 30% salt water solution to obtain a 90-gallon solution of 23% salt water.
Let's break down the problem into known values and variables:
Let x be the amount of fresh water (in gallons) to be mixed.
30% salt water solution: This means it contains 30% salt and 70% water.
23% salt water solution: This means it contains 23% salt and 77% water.
We know that the total volume of the mixture should be 90 gallons.
Now, let's set up the equation to solve for x:
Amount of salt in the 30% salt water solution + Amount of salt in the fresh water = Amount of salt in the 90-gallon 23% salt water solution
(30% of the volume of the solution) + (0% of the volume of fresh water) = (23% of 90 gallons)
0.3(90 - x) + 0(x) = 0.23(90)
Let's solve the equation:
27 - 0.3x + 0 = 20.7
-0.3x = 20.7 - 27
-0.3x = -6.3
x = -6.3 / -0.3
x = 21
Therefore, you need to mix 21 gallons of fresh water with the 30% salt water solution to obtain 90 gallons of a 23% salt water solution.