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 = ![x](https://tex.z-dn.net/?f=x)
So, number of gallons of 30% salt solution mixed will be = ![45-x](https://tex.z-dn.net/?f=45-x)
Amount of salt in
gallons of 4% salt solution will be :
<em>⇒ Percentage concentration x Gallons of solution</em>
⇒ ![0.04\times x](https://tex.z-dn.net/?f=0.04%5Ctimes%20x)
⇒ ![0.04x](https://tex.z-dn.net/?f=0.04x)
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:
⇒ ![0.04x+13.5-0.3x](https://tex.z-dn.net/?f=0.04x%2B13.5-0.3x)
Combining like terms
⇒ ![-0.26x+13.5](https://tex.z-dn.net/?f=-0.26x%2B13.5)
Amount of salt in 45 gallons of 18.4% solution:
⇒ ![0.184\times 45](https://tex.z-dn.net/?f=0.184%5Ctimes%2045)
⇒ ![8.28](https://tex.z-dn.net/?f=8.28)
Thus, we have:
![-0.26x+13.5=8.28](https://tex.z-dn.net/?f=-0.26x%2B13.5%3D8.28)
Subtracting both sides by 13.5
![-0.26x+13.5-13.5=8.28-13.5](https://tex.z-dn.net/?f=-0.26x%2B13.5-13.5%3D8.28-13.5)
![-0.26x=-5.22](https://tex.z-dn.net/?f=-0.26x%3D-5.22)
Dividing both sides by -0.26.
![\frac{-0.26x}{-0.26}=\frac{-5.22}{-0.26}](https://tex.z-dn.net/?f=%5Cfrac%7B-0.26x%7D%7B-0.26%7D%3D%5Cfrac%7B-5.22%7D%7B-0.26%7D)
∴ ![x=20.08](https://tex.z-dn.net/?f=x%3D20.08)
Number of gallons of 4% salt solution in the mixture = 20.08
Number of gallons of 30% salt solution in the mixture =
= 24.92