Question

One canned juice drink is 15​% orange​ juice; another is 10​% orange juice. How many liters of each should be mixed together in order to get 5L that is 13​% orange​ juice?

Answer 1

Answer:

3 liters of 15% and 2 liters of 10%

Step-by-step explanation:

You can set up a table that says the number of liters multiplied by the percent juice equals total percent of juice in L liters:

              L      *      % juice    =         %L

That is the main set up for the table.  We will put in values for the percent juice right away, because they were given to us.  Remember that percentages need to be expressed as decimals in order to use them in equations.

              L     *       % juice       =        %L

15%                          .15

10%                          .10

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13%                           .13

Easy enough so far.  We know that the 15% juice canned juice contains 15% juice.  No secrets there at all.  We also made a row for the mixture that needs to be 13% juice.  Next we know that the total amount of the mixture has to be 5 liters.  If we mix one juice with another and the total has to be 5 liters, then we have an unknown amount of one juice, and 5 - that unknown amount of the other juice.  Filling in we have:

             L      *      % juice       =       %L

15%        x                   .15

10%      5 - x                .10

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13%         5                   .13

Our equation tells us that we have to multiply the L times the % to fill in that last column:

             L      *      % juice      =       %L

15%        x     *          .15           =      .15x

10%      5-x    *          .10          =     .10(5 - x)

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13%         5      *        .13           =     .65

We are told from the problem we are adding the 2 juices to get the mixture, so we will add the rows in the last column and set it equal to .65:

.15x + .10(5 - x) = .65

Let's multiply everything by 100 to get rid of all those decimals:

15x + 10(5 - x) = 65

Distributing and combining like terms:

15x + 50 - 10x = 65 and

5x = 15

x = 3

That means that we need 3 liters of the canned juice that is 15% juice.

5 - 3 = 2...and 2 liters of the canned juice that is 10% juice to get the correct number of liters of 13% juice.