SOLUTION: "How many litres of 22% salt solution must be added to 80 L of 65% salt solution to obtain a 42% salt solution?" This is a review package, and this question is from my first unit

Question 557092: "How many litres of 22% salt solution must be added to 80 L of 65% salt solution to obtain a 42% salt solution?"
This is a review package, and this question is from my first unit of the year. I have totally forgotten how to solve this type of question so I would be very thankful to have the steps to an answer given!
Thank you very much!
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x = the number of liters of 22% salt.
your equation becomes:
.22 * x + .65 * 80 = .42 * (x + 80)
simplify this equation to get:
.22 * x + 52 = .42 * x + 33.6
subtract .22 * x from both sides of the equation and subtract 33.6 from both sides of the equation to get:
52 - 33.6 = .42 * x - .22 * x
combine like terms to get:
18.4 = .2 * x
divide both sides of this equation by .2 to get:
92 = x
you have x = 92
that's how many liters of 22% salt solution that you have to add to 80 liters of 65% salt solution to get a 42% salt solution.
to confirm, go back to the original equation and solve using that value of x that you calculated.
your original equation is:
.22 * x + .65 * 80 = .42 * (x + 80)
substituting 92 for x makes the equation become:
.22 * 92 + .65 * 80 = .42 * 172
simplify to get:
20.24 + 52 = 72.24
combine like terms to get:
72.24 = 72.24
this confirms the value for x is good.

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