A resturant has 161L of a cleaning solution which consists of 22% water and the remaining amount is soap. How much water is needed to be added to obtain a 55% water mixture.
let the amount of water added be x L
look at it from the view of the constant amount of soap which does not change.
.78(161) + 0x = .55(161+x)
125.58 = 88.55 + .55x
x = 67.33 L of pure water to be added
thanks, but i still dont know why you did 0.78(161)
If 22% of the original solution is water than the other part must be 78%
(22% + 78% = 100%, 100% would be the "whole thing")
and 78% = .78
so the amount of soap in the original 161L is .78(161)L = 125.58 L
This does not change, since we are adding x L of pure water
so our amount of soap is still 125.58
which is the left side of my equation: .78(161) + 0*x
but what is that ????
we now have 161L + xL = 161+x
55% of that is supposed to be soap, thus my right side of the
equation is .55(161+x)
TahDah!!!!
To solve this problem, we need to determine the amount of water needed to be added to the cleaning solution in order to achieve a 55% water mixture. Here's how we can calculate it:
Step 1: Let's determine the amount of soap in the original cleaning solution. We know that the cleaning solution consists of 22% water, which means that the remaining percentage corresponds to the soap. Therefore, the soap makes up 100% - 22% = 78% of the cleaning solution.
Step 2: We need to find out how much soap is present in the 161L of the cleaning solution. To do this, we will calculate 78% of 161L:
Amount of soap in the solution = 0.78 × 161L = 125.58L
Step 3: Now, we can determine how much water needs to be added to reach a 55% water mixture. We want to find the difference between the desired water percentage (55%) and the current water percentage (22%). This represents the amount of water that needs to be added.
Difference in water percentage = 55% - 22% = 33%
Step 4: We can calculate the amount of water needed to achieve the desired 55% water mixture by multiplying the amount of soap with the appropriate ratio of water to soap (33/78):
Amount of water needed = (33/78) × 125.58L = 53.43L
Therefore, to obtain a 55% water mixture, 53.43L of water needs to be added to the cleaning solution.