Mixture: Using the Real World Method to Solve

Math Standards: A.CED.2; A.CED.3; A.REI.11

CTE Standards:  FPP.03.01; FPP.04.01; FPP.04.03

Teacher Note:  The interest in this problem is the use of the Pearson Square method to solve.  It is the commonly taught solution method in Agriculture classes at the college level.  It is interesting that most math teachers are unaware of this solution method and instead use a system of equations solution method.  The question that I ponder is which way should I  demonstrate, the math way or the business agriculture method?

CTE Situation (opener):  When making maple confections the amount of invert sugar will affect the quality of the confection. Invert sugar syrup is a mixture of glucose and fructose; it is obtained by splitting sucrose into these two components. Inverted sugar is sweeter and its products tend to retain moisture and are less prone to crystallization making it valuable to bakers.  By measuring the invert sugar and blending different batches of syrup you will get the optimal invert sugar outcome for the confection.

The ideal invert sugar measurement for maple candy is 1%. If we have light syrup that has .5% invert sugars and dark syrup with 2.2% invert sugars. What mixture of light and dark syrup do you need to reach the desired invert sugar level of 1% to make maple candy?

 

Pearson Square Method Solution

square

The value in the middle of the square (the goal of the mixture) must be intermediate between the two values that are used on the left side of the square.  The numbers on the right side of the square are obtained by subtracting diagonally smallest from largest.  The denominator is the sum of the numbers on the right side of the square.

Solution using systems of equations:

.5L + 2.2D= 1

L + D= 1

Solution:

.5L + 2.2D=1

-.5L – .5D= -.5

1.7D=.5

D=.294 or 29.4% Dark

L + .294=1

 

L=.706 or 70.6% Light

Thanks to Erin McCaffrey and Jeannie McLean of Stockbridge Valley Schools of Munnsville NY for creating this for others to use.