Math Standards: A.CED.2; A.CED.3; A.REI.11
CTE Standards: FPP.03.01; FPP.04.01; FPP.04.03
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?
Solution
using Pearson Square Method:
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:
Solve
the following system of equations:
.5L + 2.2D= 1
L
+ D= 1
Solution: Answer:
.5L
+ 2.2D=1 29.4%
Dark
-.5L
– .5D= -.5 70.6%
Light
1.7D=.5
D=.294
L
+ .294=1
L=.706
Thanks to Erin McCaffrey and Jeannie McLean of Stockbridge Valley Schools of Munnsville NY
