Answer:
Number of gallons of 4% salt solution in the mixture = 20.08
Number of gallons of 30% salt solution in the mixture = 24.92
Step-by-step explanation:
Given:
There are two bottles of brine solution:
1 has 4% salt
2 has 30% salt
The chemist mixes some gallons of each bottle to get a 45 gallons solution containing 18.4% salt.
To find the gallons of each solution taken to make the mixture.
Solution:
Let the number of gallons of 4% salt solution mixed be =
So, number of gallons of 30% salt solution mixed will be =
Amount of salt in gallons of 4% salt solution will be :
<em>⇒ Percentage concentration x Gallons of solution</em>
⇒
⇒
Amount of salt in gallons of 30%% salt solution will be :
<em>⇒ Percentage concentration x Gallons of solution</em>
<em>⇒ </em><em />
Using distribution
<em>⇒ </em><em />
Total amount of salt in 45 gallons of solution can be given as:
⇒
Combining like terms
⇒
Amount of salt in 45 gallons of 18.4% solution:
⇒
⇒
Thus, we have:
Subtracting both sides by 13.5
Dividing both sides by -0.26.
∴
Number of gallons of 4% salt solution in the mixture = 20.08
Number of gallons of 30% salt solution in the mixture = = 24.92