Question

A chemist has two brine solutions, one containing 4% salt and the other containing 30% salt. How many gallons of each solution should she mix to obtain 45 gallons of a solution that contains 18.4% salt?

Answer 1

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  = $x$

So, number of gallons of 30% salt solution mixed will be = $45-x$

Amount of salt in $x$ gallons of 4% salt solution will be :

⇒ Percentage concentration x Gallons of solution

⇒ $0.04\times x$

⇒ $0.04x$

Amount of salt in $(45-x)$ gallons of 30%% salt solution will be :

⇒ Percentage concentration x Gallons of solution

⇒ $0.3\times (45-x)$

Using distribution

⇒ $13.5-0.3x$

Total amount of salt in 45 gallons of solution can be given as:

⇒ $0.04x+13.5-0.3x$

Combining like terms

⇒ $-0.26x+13.5$

Amount of salt in 45 gallons of 18.4% solution:

⇒ $0.184\times 45$

⇒ $8.28$

Thus, we have:

$-0.26x+13.5=8.28$

Subtracting both sides by 13.5

$-0.26x+13.5-13.5=8.28-13.5$

$-0.26x=-5.22$

Dividing both sides by -0.26.

$\frac{-0.26x}{-0.26}=\frac{-5.22}{-0.26}$

∴ $x=20.08$

Number of gallons of 4% salt solution in the mixture = 20.08

Number of gallons of 30% salt solution in the mixture = $45-20.08$ = 24.92