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Percent Concentrations - Problem 2

Teacher/Instructor Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

In this problem I’m going to be mixing two different kinds of lemonade that have two different concentrations to get some kind of mixture. For a graduation party Amelia mixed 9 gallons of brand A lemonade with 6 gallons of brand B lemonade. Brand A contains 28% real fruits juice and brand B contains 18% real fruit juice. What percent of the mixture is real fruit juice?

Well I’m going to use the formula amount times concentration plus amount times concentration equals mixture amount plus mixture concentration. Here's my first ingredient amount times concentration that's brand A lemonade and I wrote 28% as .2 8.

To that I’m adding brand B amount times concentration to get my mixture amount. Well the mixture amount is kind of tricky because you have to keep in mind what's going on you are adding brand A plus brand B so my mixture amount is going to be 9 plus 6 which is 15.

Then I need my mixture concentration that's what I’m solving for it, it says what percent of the mixture is real fruit juice there we go. Here we go now I’m ready to solve this is an easy just plug and chug simplifying grab your calculator and start doing 9 times .2 8 by the way this is why it's really important that you write these using this percents using decimals instead of using the percent sign otherwise your calculator is not going to do it in a way that makes sense to you.

Okay 1. 08 is equal to 15x combine those and you get 3.6 equals 15x. Divide both sides by 15 and you get your percent concentration .24. So if you want to you can write it like that or you might want to say 24% real fruit juice keep in mind the 24% is the same thing as .24 and make sure you label your answer with words you don't want to just write x equals .24 you want to label it.

.24 is how much real fruit juice there is in my mixture of lemonades. So this one is a little bit different because I knew both the amounts of concentration in my ingredients but I had to find the amount in concentration of my mixture.

It’s the same type of formula that we've been using for all of these mixture problems and that is amount times concentration 1 plus amount times concentration 2 equals the amount of the mixture times the concentration of the mixture.

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