Question

How many gallons of a 42% salt solution do we need to mix with 98 gallons of a 20% salt solution so that the resulting mixture is a 28% salt solution ?

Answer 1

56

Explanation:

98 gallons of a 20 percent salt solution results in 20/100 * 98 = 19.6 gallons of salt.

Let's say we need x gallons of the 42% salt solution.

To make sure that the resulting mixture has 28% salt, we need to have the total salt divided by the total amount of gallons.

We have 98 total gallons in the first solution, and x total gallons in the second solution. We have 19.6 gallons of salt in the first solution and 42% of x gallons in the second solution:

`19.6+(42)/(100)(x)=(28)/(100)(98+x)`

Expanding, we have

`19.6+(42)/(100)x=27.44+(28)/(100)x`

Subtracting 19.6 and subtracting 28/100x from both sides equals

`(14)/(100)x=7.84`

Multiplying both sides by 100:

`14x=784`

Dividing both sides by 14:

`x=56`