The royal fruit company produces two types of fruit drinks. the first type is 30 % pure fruit juice, and the second type is 55 % pure fruit juice. the company is attempting to produce a fruit drink that contains 40 % pure fruit juice. how many pints of each of the two existing types of drink must be used to make 170 pints of a mixture that is 40 % pure fruit juice?

Step-by-step explanation:

Make a table to solve this.  Mixture tables are always the same as far as what goes into each column.  The first column will contain the number of either pounds, or gallons, or liters, or (in our case) pints.  The second column will always be either the cost or percent per pound, gallon, liter, or (in our case) pint.  The last column will be the product of the first 2 columns.  Our table:

                 # pints        x         % juice           =         pints of juice

Juice 1

Juice 2

Mix

We can fill in the percentage of juice for all three juices first:

                # pints          x          % juice          =          pints of juice

Juice 1                                          .30

Juice 2                                         .55

Mix                                               .40

If we want to make a total of 170 pints of the mix, then 170 goes into the first column, last row:

                # pints           x           % juice          =           pints of juice

Juice 1                                              .30

Juice 2                                             .55

Mix                170            x                .40            =                  68

If we are to make a total of 170 pints and we don't know how much of either Juice 1 or Juice 2 we have, we will have x amount of juice 1 and 170-x amount of Juice 2.  I will fill that in along with the last column which is the product of the first 2.  I already did that in the last row.  170 * .40 = 68.

                   # pints           x           % juice             =               pints of juice

Juice 1              x                x              .30                =                   .30x

Juice 2       170-x               x              .55                =              93.5 - .55x

Mix                170               x              .40                =                     68

We are adding Juice 1 and Juice 2 to get the mix, so that is what we will do with the last column...add them and set them equal to the mix:

.30x + 93.5 - .55x = 68 and

-.25x = -25.5 so

x = 102 pints

That means that there needs to 102 pints of 30% juice mixed with 68 pints of 55% juice to get 170 pints of juice that is 40% juice.