Mathnasium discusses Chocolate Mixes.

The confectionary shelves at the super markets are brimming with all sorts of Easter themed goodies. Chocolate eggs and bunnies dominate the scene as a holdover from ancient pagan celebrations to the gods of fertility; and birth that accompany the renewal of Spring. We're anticipating Easter too! Our photograph is a limited edition chocolate Easter egg from the French pastry super chef Pierre Hermé. It's inspired us to ask this word problem.

A chocolatier receives an order for a 10-pound chocolate statue whose cacao content is exactly 40%. The chocolatier has 20% cacao chocolate and 50% cacao chocolate at his disposal. How many pounds of each does he need to melt together to have exactly the right amount for the statue?

Pierre Hermé—whose nickname is the Picasso of pastry—built that Easter Egg from from Brazilian dark chocolate. It is a homage to the paintings and metal sculptures of Swiss artist Beat Zoderer. The multicolored ribbons of chocolate that look like rubber bands are flavored with citrus, red berries, and spices; and are stretched across a chocolate shell containing a secret drawer with even more chocolote!

At Mathnasium, we have this statement:

An expert is a man who has made all the mistakes which can be made, in a narrow field.~ Niels Bohr

Pierre embodies that statement. He has dedicated himself to a lifetime of experimentation with chocolate. He and his team have learned how various forms of chocolate behave. They have exploited those behaviours to delight us. That experimentation is how scientist discover "secrets" of matter; and in turn, engineers use those discoveries to create products. Yes, Pierre is an experimental-scientist, engineer, architect, and artist (and entrepreneur) in his domain of chocolate and pastries.

Let's see how Pierre has to use math to solve this word problem. The whole is the sum of its parts. He will need x pounds of 20% chocolate and y pounds of 50% chocolate. The whole sculpture weighs 10 pounds; or
x + y = 10 pounds; or
(1) x = 10 - y
Chocolate is a mix of cocoa, and other yumminess. The cocoa portion is 20% of x + 50% of y = 40% of 10 pounds; or
(2) 0.2x + 0.5y = 4
Substitute (1) into (2)
0.2(10 - y) + 0.5y = 4
2 - 0.2y + 0.5y = 4
0.3y = 2
y = 20/3 = 6 ⅔ pounds of 50% chocolate.
From (1), x = 10 - y = 10 - 6 ⅔ = 3 ⅓ pounds of 20% chocolate.

If that puzzles your chocolate cravings, come to Mathnasium and we'll be happy to explain it to you... the math, not the cravings.

Contact:
Ruby Yao and Benedict Zoe, Mathnasium of Fort Lee
201-969-6284 (WOW-MATH), fortlee@mathnasium.com
246 Main St. #A
Fort Lee, NJ 07024
Happily serving communities of Cliffside Park, Edgewater, Fort Lee, Leonia, and Palisades Park.